{"ok":true,"count":200,"questions":[{"id":25516,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"砖雕是一种历史悠久的古建筑装饰艺术，是 第一批国家级非物质文化遗产．图是一块扇\\(1 \\frac{2}{O}\\)面形的砖雕作品，它的部分设计图如图所示，\\(\\frac{其中扇形}{圆心角}\\frac{OBC}{120} \\frac{OAD}{OA}\\)和扇形 有相同的圆心，且 O = ，若 = cm,OB = 30cm，\\(\\frac{90}{cm^{2}}\\)则阴影部分的面积是 ____。（结果用表 示）","options":[],"answer":"．","solution":" 圆心角O =120, = 90, = cm，\\(\\frac{OA}{120} \\frac{cmOB}{90^{2}} \\frac{30}{120}\\) \\(30^{2}\\)阴影部分的面积是 − =\\(\\frac{360}{cm^{2}} \\frac{360}{2400} 2700− 300= 2400()\\)故答案为： ．","stem_html":"<div>砖雕是一种历史悠久的古建筑装饰艺术，是 第一批国家级非物质文化遗产．图是一块扇\\(1 \\frac{2}{O}\\)面形的砖雕作品，它的部分设计图如图所示，\\(\\frac{其中扇形}{圆心角}\\frac{OBC}{120} \\frac{OAD}{OA}\\)和扇形 有相同的圆心，且 O = ，若 = cm,OB = 30cm，\\(\\frac{90}{cm^{2}}\\)则阴影部分的面积是 ____。（结果用表 示）<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/f62c0ba5-4911-44f1-9c8c-88bf6d514736/02ec0d59f39f.png\" style=\"width:349.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"．","solution_html":" 圆心角O =120, = 90, = cm，\\(\\frac{OA}{120} \\frac{cmOB}{90^{2}} \\frac{30}{120}\\) \\(30^{2}\\)阴影部分的面积是 − =\\(\\frac{360}{cm^{2}} \\frac{360}{2400} 2700− 300= 2400()\\)故答案为： ．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:41:24"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:41:24"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:41:24"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T10:41:44"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T10:41:59"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T10:41:59"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:41:59"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:43:25"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T10:43:25"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T10:47:06"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:47:06"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T10:48:11"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:48:11"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:48:11"}],"detail_url":"/questions/25516","edit_url":"/questions/25516/edit","json_url":"/api/questions/25516","recheck_url":"/api/questions/25516/recheck"},{"id":25517,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"【小试1】 如图，等边△ABC是⊙O的内接三角形，若⊙O的半径为4，则阴影 部分的面积为________．","options":[],"answer":"_{3}−4√3","solution":"连接OB、OC，连接AO并延长并BC于点D，如下图，则AD ⊥BC．因为等边△ABC是⊙ O的内接三角形，∴∠OCD = 30∘，∴OD = 2, ∠COD=60∘, ∴BD = CD =\\(\\sqrt{4^{2}}\\)−\\(2^{2}\\)= 2√3, ∠BOC = 1 1 ∠AOB = 120∘, ∴S△BOC=_{2}BC ⋅OD = _{2}\\(\\times 2 \\times 2√3 \\times 2 = 4√3\\)∴S△AOB= S△BOC= 4√3, ∴图中阴\\(120\\pi\\times 42 16\\pi 16\\pi\\)影部分的面积 = 360 −4√3 = _{3}−4√3. 故答案为: _{3}−4\\(\\sqrt{3. \\pi}\\)","stem_html":"<div>【小试1】 如图，等边△ABC是⊙O的内接三角形，若⊙O的半径为4，则阴影 部分的面积为________．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/d96e74fd-8f90-4b62-ae99-972364836672/c399fdca0c4e.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"_{3}−4√3","solution_html":"连接OB、OC，连接AO并延长并BC于点D，如下图，则AD ⊥BC．因为等边△ABC是⊙ O的内接三角形，∴∠OCD = 30∘，∴OD = 2, ∠COD=60∘, ∴BD = CD =\\(\\sqrt{4^{2}}\\)−\\(2^{2}\\)= 2√3, ∠BOC = 1 1 ∠AOB = 120∘, ∴S△BOC=_{2}BC ⋅OD = _{2}\\(\\times 2 \\times 2√3 \\times 2 = 4√3\\)∴S△AOB= S△BOC= 4√3, ∴图中阴\\(120\\pi\\times 42 16\\pi 16\\pi\\)影部分的面积 = 360 −4√3 = _{3}−4√3. 故答案为: _{3}−4\\(\\sqrt{3. \\pi}\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:45:02"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:45:02"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:45:02"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T10:45:15"},{"type":"SOLVER","status":"PASS","score":0.85,"created_at":"2026-09-26T10:45:23"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T10:45:23"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:45:23"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:46:00"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T10:46:00"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T10:46:47"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:46:47"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:48:05"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-09-26T10:48:05"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.85,"created_at":"2026-09-26T10:48:05"}],"detail_url":"/questions/25517","edit_url":"/questions/25517/edit","json_url":"/api/questions/25517","recheck_url":"/api/questions/25517/recheck"},{"id":25524,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"一个扇形的圆心角为\\(120^\\circ\\), 弧长为\\(6\\pi\\)cm, 则该扇形的面积为____cm\\(^2\\)．","options":[],"answer":"","solution":"","stem_html":"<div>一个扇形的圆心角为\\(120^\\circ\\), 弧长为\\(6\\pi\\)cm, 则该扇形的面积为____cm\\(^2\\)．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:42:57"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:42:57"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:42:57"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:43:02"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:43:32"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:43:32"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:43:32"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:43:46"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:43:46"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T10:46:06"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:46:06"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:47:25"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:47:25"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:47:25"}],"detail_url":"/questions/25524","edit_url":"/questions/25524/edit","json_url":"/api/questions/25524","recheck_url":"/api/questions/25524/recheck"},{"id":25522,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[4,5],"stem":"山西现存全国重点文物保护单位531处，居全国第一．古建筑屋顶的国瓦当发展历程悠久，其艺术风格和功能随着历史时期的变化而演变．现有一瓦当，它的一面是呈扇形的一部分，如图1所示，其中两边AB, CD所在直线构成的夹角∠AOD = 90∘，点O是扇形所在圆的圆心，AO = DO=18cm, BO = CO = 10cm如图2所示，则该瓦当此面的面积为____cm^{2}。（结果保留\\(\\pi）\\)","options":[],"answer":"","solution":"","stem_html":"<div>山西现存全国重点文物保护单位531处，居全国第一．古建筑屋顶的国瓦当发展历程悠久，其艺术风格和功能随着历史时期的变化而演变．现有一瓦当，它的一面是呈扇形的一部分，如图1所示，其中两边AB, CD所在直线构成的夹角∠AOD = 90∘，点O是扇形所在圆的圆心，AO = DO=18cm, BO = CO = 10cm如图2所示，则该瓦当此面的面积为____cm^{2}。（结果保留\\(\\pi）\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/e69c58b2-91f3-482c-a558-0658be60fb45/05f45341b216.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:39:47"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:39:47"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:39:47"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:40:29"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T10:43:08"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:43:08"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:43:08"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:43:25"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T10:43:25"}],"detail_url":"/questions/25522","edit_url":"/questions/25522/edit","json_url":"/api/questions/25522","recheck_url":"/api/questions/25522/recheck"},{"id":25523,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，点A在⊙O的直径CD的延长线上，点B在⊙O上，连接AB, BC. 若AB是⊙O的切线，AB = BC = 6, ∠ABC = 120∘, 则图中阴影部分的面积是____．","options":[],"answer":"","solution":"","stem_html":"<div>如图，点A在⊙O的直径CD的延长线上，点B在⊙O上，连接AB, BC. 若AB是⊙O的切线，AB = BC = 6, ∠ABC = 120∘, 则图中阴影部分的面积是____．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/ca4cfb46-def7-4cdb-83b1-18d52b78e470/7630d624e0f1.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:39:27"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:39:27"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:39:27"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:39:39"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T10:43:07"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:43:07"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:43:07"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:43:20"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T10:43:20"}],"detail_url":"/questions/25523","edit_url":"/questions/25523/edit","json_url":"/api/questions/25523","recheck_url":"/api/questions/25523/recheck"},{"id":25521,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"中国是个重视孝道的国家，＂孝＂是我国传统的美德．如图①是一 块弘扬＂孝＂的扇面宣传展板，该展板的部分示意图如图②所示 ，点C、D分别在OA、OB上，AB与CD都是以O为圆心，OA、OC长分别为半径，圆心角∠O = 62∘，若OA = 4m, OC = 2m，则阴影部分的面积为____m^{2}．（结果保留\\(\\pi）\\)","options":[],"answer":"","solution":"","stem_html":"<div>中国是个重视孝道的国家，＂孝＂是我国传统的美德．如图①是一 块弘扬＂孝＂的扇面宣传展板，该展板的部分示意图如图②所示 ，点C、D分别在OA、OB上，AB与CD都是以O为圆心，OA、OC长分别为半径，圆心角∠O = 62∘，若OA = 4m, OC = 2m，则阴影部分的面积为____m^{2}．（结果保留\\(\\pi）\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/82dd6146-f7a0-476e-af62-c5658d792206/092392602a6c.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:38:41"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:38:41"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:38:41"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:38:58"}],"detail_url":"/questions/25521","edit_url":"/questions/25521/edit","json_url":"/api/questions/25521","recheck_url":"/api/questions/25521/recheck"},{"id":25520,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，水平放置的圆柱形排水管道的截面半径是0.6m，其中从水面垂 直最深处0.3m，求截面中有水部分的面积。","options":[],"answer":"","solution":"","stem_html":"<div>如图，水平放置的圆柱形排水管道的截面半径是0.6m，其中从水面垂 直最深处0.3m，求截面中有水部分的面积。<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/7cbbb8a7-444b-4c5e-bffa-158cd63a653e/4e9cfe45fa0c.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-09-26T10:37:39"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:37:39"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:37:39"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:38:08"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T10:38:35"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T10:38:35"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:38:35"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:38:58"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T10:38:58"}],"detail_url":"/questions/25520","edit_url":"/questions/25520/edit","json_url":"/api/questions/25520","recheck_url":"/api/questions/25520/recheck"},{"id":25504,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"扇形的面积：____________________","options":[],"answer":"S =\\(\\frac{1}{2}lr = \\frac{n\\pi r^{2}}{360}\\)","solution":"根据《核心知识点》原文第1条，扇形面积公式为 S =\\(\\frac{1}{2}lr\\)或 S =\\(\\frac{n r^{2}}{360}（\\)其中n为圆心角度数，l为弧长，r为半径）。","stem_html":"<div>扇形的面积：____________________</div>","answer_html":"S =\\(\\frac{1}{2}lr = \\frac{n\\pi r^{2}}{360}\\)","solution_html":"根据《核心知识点》原文第1条，扇形面积公式为 S =\\(\\frac{1}{2}lr\\)或 S =\\(\\frac{n r^{2}}{360}（\\)其中n为圆心角度数，l为弧长，r为半径）。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:34:13"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:34:13"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:34:13"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:34:28"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:34:28"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T10:34:50"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:34:50"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:35:13"},{"type":"QUALITY_GATE","status":"PASS","score":0.925,"created_at":"2026-09-26T10:35:13"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:36:00"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:36:00"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:37:02"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:37:02"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T10:37:02"}],"detail_url":"/questions/25504","edit_url":"/questions/25504/edit","json_url":"/api/questions/25504","recheck_url":"/api/questions/25504/recheck"},{"id":25492,"job_id":3,"qa_status":"QUARANTINED","question_type":"knowledge","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":1.0,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1480.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"三角形面积=\\(\\frac{1}{2}\\times\\)底\\(\\times\\)高 quad (n 是扇形圆心角度数，l是弧长，r是扇形半径)","options":[],"answer":"","solution":"","stem_html":"<div>三角形面积=\\(\\frac{1}{2}\\times\\)底\\(\\times\\)高<span class=\"formula-fallback\">quad (n</span>是扇形圆心角度数，l是弧长，r是扇形半径)</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-09-26T10:34:11"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-09-26T10:34:11"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:34:37"},{"type":"QUALITY_GATE","status":"FAIL","score":1.0,"created_at":"2026-09-26T10:34:37"}],"detail_url":"/questions/25492","edit_url":"/questions/25492/edit","json_url":"/api/questions/25492","recheck_url":"/api/questions/25492/recheck"},{"id":25480,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.65,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1475.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"5.如图，已知\\(\\widehat{AB},\\widehat{CD}\\)的弧长之差为\\(4\\pi\\)，\\(\\angle AOB= 120^\\circ\\)，若\\(OC = 15\\)，则阴影部分的周长为 ______.","options":[],"answer":"\\(120\\pi⋅\\)OA\\(120\\pi⋅\\)OC","solution":"=\\(4\\pi,∴\\)OA− OC = 6,∴ AC =BD= 6,∵ 根据题意得 : − 180 180 \\(120\\pi\\times 15\\) OC = 15,∴ CD的弧长 == =\\(10\\pi,∴\\)AB的弧长 =\\(10\\pi+ 4\\pi= 14\\pi,∴ 180\\)  阴影部分的周长AC+BD+ CD的弧长 + AB的弧长6 + 6 +\\(10\\pi+ 14\\pi= 12 + 24\\pi\\)故 答案为: 12 +\\(24\\pi\\)m −\\(\\pi{}d\\)","stem_html":"<div>5.如图，已知\\(\\widehat{AB},\\widehat{CD}\\)的弧长之差为\\(4\\pi\\)，\\(\\angle AOB= 120^\\circ\\)，若\\(OC = 15\\)，则阴影部分的周长为 ______.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/e4c57b98-8193-4b2f-8c0e-3f35a04875e1/a6c63a5dae99.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"\\(120\\pi⋅\\)OA\\(120\\pi⋅\\)OC","solution_html":"=\\(4\\pi,∴\\)OA− OC = 6,∴ AC =BD= 6,∵ 根据题意得 : − 180 180 \\(120\\pi\\times 15\\) OC = 15,∴ CD的弧长 == =\\(10\\pi,∴\\)AB的弧长 =\\(10\\pi+ 4\\pi= 14\\pi,∴ 180\\)  阴影部分的周长AC+BD+ CD的弧长 + AB的弧长6 + 6 +\\(10\\pi+ 14\\pi= 12 + 24\\pi\\)故 答案为: 12 +\\(24\\pi\\)m −\\(\\pi{}d\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:22:29"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:22:29"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:22:29"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T10:23:41"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T10:25:50"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:25:50"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:25:50"},{"type":"COHERENCE","status":"FAIL","score":0.85,"created_at":"2026-09-26T10:27:10"},{"type":"QUALITY_GATE","status":"FAIL","score":0.65,"created_at":"2026-09-26T10:27:10"}],"detail_url":"/questions/25480","edit_url":"/questions/25480/edit","json_url":"/api/questions/25480","recheck_url":"/api/questions/25480/recheck"},{"id":25481,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1475.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图,在扇形AOB中, ∠AOB= 30°,点C为半径OA上一点,先以点O为圆心,OC  长为半径作弧,该弧交半径OB于点D,记AB的长为m,BD的长度为d,则  CD的长为______. (用含m，d的式子表示) 填空题，每题6分","options":[],"answer":"\\(\\pi 180 \\pi 6 6\\)","solution":"","stem_html":"<div>如图,在扇形AOB中, ∠AOB= 30°,点C为半径OA上一点,先以点O为圆心,OC  长为半径作弧,该弧交半径OB于点D,记AB的长为m,BD的长度为d,则  CD的长为______. (用含m，d的式子表示) 填空题，每题6分<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/7ee4d60a-0a2b-437b-bea5-a1062cf3f71c/d6e0b34fed07.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"\\(\\pi 180 \\pi 6 6\\)","solution_html":"","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:19:12"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:19:12"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:19:12"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T10:19:35"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T10:21:02"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:21:02"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:21:02"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:21:22"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T10:21:22"}],"detail_url":"/questions/25481","edit_url":"/questions/25481/edit","json_url":"/api/questions/25481","recheck_url":"/api/questions/25481/recheck"},{"id":25485,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1475.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图，已知扇形$AOB 的面积为\\(3π\\)，点\\(C\\)在圆周上，\\(angle ACB = 60^circ\\)，则\\(odot O\\)的半径为____．","options":[],"answer":"3","solution":"设⊙O的半径为r, ∵∠ACB = 60∘, ∴∠AOB = 2∠ACB = 120∘, ∵扇形AOB的\\(120\\pi \\timesr^{2}\\)面积为\\(3\\pi,∴ = 3\\pi\\)解得r= 3(负值已舍去),即 ⊙ O的半径为3,故答案为 : 3．\\(360 \\pi / \\frac{1}{3} \\pi\\)","stem_html":"<div>如图，已知扇形$AOB<span class=\"formula-fallback\">的面积为\\(3π\\)，点\\(C\\)在圆周上，\\(angle ACB = 60^circ\\)，则\\(odot O\\)的半径为____．</span><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/67e53d04-1378-456f-b77d-aac9d6767b83/de90522f5621.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"3","solution_html":"设⊙O的半径为r, ∵∠ACB = 60∘, ∴∠AOB = 2∠ACB = 120∘, ∵扇形AOB的\\(120\\pi \\timesr^{2}\\)面积为\\(3\\pi,∴ = 3\\pi\\)解得r= 3(负值已舍去),即 ⊙ O的半径为3,故答案为 : 3．\\(360 \\pi / \\frac{1}{3} \\pi\\)","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:23:48"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-09-26T10:23:48"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:23:48"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T10:24:03"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:24:17"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:24:17"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:24:17"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T10:25:02"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:25:02"}],"detail_url":"/questions/25485","edit_url":"/questions/25485/edit","json_url":"/api/questions/25485","recheck_url":"/api/questions/25485/recheck"},{"id":25482,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1475.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"在半径为18cm的圆上有一段弧,弧长是\\(12\\pi{}cm\\)则该弧所对的圆周角的度数为 ____．","options":[],"answer":"60°/60度","solution":"\\(n\\pi{}rn\\pi\\times 18\\)根据弧长的公式l=,得到：\\(12\\pi=\\)解得n = 120∘, 故圆周角为60∘故答案为：60∘． 180 180","stem_html":"<div>在半径为18cm的圆上有一段弧,弧长是\\(12\\pi{}cm\\)则该弧所对的圆周角的度数为 ____．</div>","answer_html":"60°/60度","solution_html":"\\(n\\pi{}rn\\pi\\times 18\\)根据弧长的公式l=,得到：\\(12\\pi=\\)解得n = 120∘, 故圆周角为60∘故答案为：60∘． 180 180","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:19:22"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:19:22"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:19:22"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:19:45"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:19:45"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T10:19:51"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-09-26T10:19:51"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:20:48"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T10:20:48"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:22:48"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:22:48"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:24:32"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:24:32"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T10:24:32"}],"detail_url":"/questions/25482","edit_url":"/questions/25482/edit","json_url":"/api/questions/25482","recheck_url":"/api/questions/25482/recheck"},{"id":25477,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1475.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"\\(4\\pi 2\\).将一把折扇展开,可抽象成一个扇形,若该扇形的半径为2,弧长为,则扇形的圆心角大小为( ) 3 A. 30∘ B. 60∘ C. 90∘ D. 120∘","options":[{"label":"A","text":"30∘"},{"label":"B","text":"60∘"},{"label":"C","text":"90∘"},{"label":"D","text":"120∘"}],"answer":"D","solution":"\\(4\\pi{}n\\pi{}r\\)扇形的半径为2,弧长为,弧长公式l= (l是弧长,n是圆心角度数,r 3 180 180∘l 180∘\\(\\times ^{4}\\pi\\)是扇形半径)， ∴ n= = 3 = 120∘, 故选: D．\\(\\pi{}r 2\\pi\\)","stem_html":"<div>\\(4\\pi 2\\).将一把折扇展开,可抽象成一个扇形,若该扇形的半径为2,弧长为,则扇形的圆心角大小为(     ) 3<br>A. 30∘<br>B. 60∘<br>C. 90∘<br>D. 120∘</div>","answer_html":"D","solution_html":"\\(4\\pi{}n\\pi{}r\\)扇形的半径为2,弧长为,弧长公式l= (l是弧长,n是圆心角度数,r 3 180 180∘l 180∘\\(\\times ^{4}\\pi\\)是扇形半径)， ∴ n= = 3 = 120∘, 故选: D．\\(\\pi{}r 2\\pi\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:19:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:19:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:19:11"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T10:19:28"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:20:00"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:20:00"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:20:00"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:20:29"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T10:20:29"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:21:11"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:21:11"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:22:48"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:22:48"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T10:22:48"}],"detail_url":"/questions/25477","edit_url":"/questions/25477/edit","json_url":"/api/questions/25477","recheck_url":"/api/questions/25477/recheck"},{"id":25479,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1475.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"如图, 用一个半径为3cm的定滑轮带动重物上升, 滑轮上一点P旋转了90∘,假设 绳索(粗细不计)与滑轮之间没有滑动, 则重物上升了____ cm. (结果保留\\(\\pi\\))","options":[],"answer":"\\(1.5\\pi\\)","solution":"弧长公式为 l = (\\(n\\pi{}r\\))/180，其中 n = 90，r = 3 cm。代入得 l = (\\(90\\pi \\times 3\\))/180 =\\(1.5\\pi\\)cm。由于绳索与滑轮之间无滑动，重物上升的距离等于滑轮上点P旋转的弧长，因此重物上升了\\(1.5\\pi\\)cm。","stem_html":"<div>如图, 用一个半径为3cm的定滑轮带动重物上升, 滑轮上一点P旋转了90∘,假设 绳索(粗细不计)与滑轮之间没有滑动, 则重物上升了____ cm. (结果保留\\(\\pi\\))<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/10a3a2f2-fdfe-4fde-b608-0e984ab46fa1/99ed37cd4846.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"\\(1.5\\pi\\)","solution_html":"弧长公式为 l = (\\(n\\pi{}r\\))/180，其中 n = 90，r = 3 cm。代入得 l = (\\(90\\pi \\times 3\\))/180 =\\(1.5\\pi\\)cm。由于绳索与滑轮之间无滑动，重物上升的距离等于滑轮上点P旋转的弧长，因此重物上升了\\(1.5\\pi\\)cm。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:19:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:19:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:19:50"},{"type":"VISION","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:20:20"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:20:24"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:20:24"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:20:24"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:20:53"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T10:20:53"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:21:39"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:21:39"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T10:22:17"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:22:17"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T10:22:17"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-09-26T10:22:17"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T10:22:39"}],"detail_url":"/questions/25479","edit_url":"/questions/25479/edit","json_url":"/api/questions/25479","recheck_url":"/api/questions/25479/recheck"},{"id":25475,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"传统服饰日益受到关注，如图1为明清时期女子主要裙式之一的马面裙，如图2马面裙可以近似地看作扇环，其中AD长度为\\(\\frac{1}{3}\\pi\\)米，BC长度为\\(\\frac{3}{5}\\pi\\)米，圆心角∠AOD = 60°，则裙长AB为______.","options":[],"answer":"","solution":"","stem_html":"<div>传统服饰日益受到关注，如图1为明清时期女子主要裙式之一的马面裙，如图2马面裙可以近似地看作扇环，其中AD长度为\\(\\frac{1}{3}\\pi\\)米，BC长度为\\(\\frac{3}{5}\\pi\\)米，圆心角∠AOD = 60°，则裙长AB为______.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/748423ef-89d5-4974-b4e1-f10b992e6222/343b9e640b6b.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:13:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:13:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:13:12"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:13:24"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:15:37"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:15:37"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:15:37"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:15:49"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:15:49"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:17:40"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:17:40"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:17:54"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:17:54"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T10:17:54"}],"detail_url":"/questions/25475","edit_url":"/questions/25475/edit","json_url":"/api/questions/25475","recheck_url":"/api/questions/25475/recheck"},{"id":25466,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图，ABC内接于半径为的6 O中作, O的 BD,若 = 50,连接OC,则图中扇形的\\(A \\frac{直径}{面积是} ()\\)．8 ．6 ．\\(\\frac{16}{9}\\)．\\(\\frac{32}{9}\\)A B C D","options":[],"answer":"","solution":": = 50, = 2=100,\\(\\frac{由题可得}{COD} \\frac{BOC}{80}\\)A A  = −BOC =,\\(\\frac{180}{80}\\)\\(6^{2}\\)S扇形 = = 8,故选 : ． A COD 360","stem_html":"<div>如图，ABC内接于半径为的6 O中作, O的 BD,若 = 50,连接OC,则图中扇形的\\(A \\frac{直径}{面积是} ()\\)．8 ．6 ．\\(\\frac{16}{9}\\)．\\(\\frac{32}{9}\\)A B C D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/31b08d59-98ae-416b-a8e8-f81d896dfd11/98f2a1ded21e.png\" style=\"width:149.0px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":": = 50, = 2=100,\\(\\frac{由题可得}{COD} \\frac{BOC}{80}\\)A A  = −BOC =,\\(\\frac{180}{80}\\)\\(6^{2}\\)S扇形 = = 8,故选 : ． A COD 360","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:10:51"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:10:51"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:10:51"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T10:11:52"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T10:12:25"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:12:25"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:12:25"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T10:12:46"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:12:46"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T10:14:54"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:14:54"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:16:15"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:16:15"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:16:15"}],"detail_url":"/questions/25466","edit_url":"/questions/25466/edit","json_url":"/api/questions/25466","recheck_url":"/api/questions/25466/recheck"},{"id":25471,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.633,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[3,4],"stem":"如图，线段AB是⊙O的直径，点C, D是圆上两点，连接AC, BD, CD，若∠D = 30°，AC = 6，则阴影部分的面积为( ) A. \\(3 _{2}\\pi\\) B. \\(2\\pi\\) C. \\(\\sqrt{3_{3}}\\pi\\) D. \\(\\pi\\)","options":[{"label":"A","text":"3 _{2}\\pi"},{"label":"B","text":"2\\pi"},{"label":"C","text":"\\sqrt{3_{3}}\\pi"},{"label":"D","text":"\\pi"}],"answer":"","solution":"","stem_html":"<div>如图，线段AB是⊙O的直径，点C, D是圆上两点，连接AC, BD, CD，若∠D = 30°，AC = 6，则阴影部分的面积为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/79663031-4f94-4093-a5cb-4eb6a8d94ef4/628e3d0d6098.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(3 _{2}\\pi\\)<br>B. \\(2\\pi\\)<br>C. \\(\\sqrt{3_{3}}\\pi\\)<br>D. \\(\\pi\\)</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:11:09"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:11:09"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:11:09"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T10:11:28"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T10:16:01"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:16:01"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:16:01"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T10:16:10"},{"type":"QUALITY_GATE","status":"FAIL","score":0.633,"created_at":"2026-09-26T10:16:10"}],"detail_url":"/questions/25471","edit_url":"/questions/25471/edit","json_url":"/api/questions/25471","recheck_url":"/api/questions/25471/recheck"},{"id":25474,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图, 某游乐场的旋转木马旋转一周需240秒, 旋转半径是6米. 旋转时,一 木马某时刻在点A处，80秒后旋转到点B. 则该木马旋转的路径长(即弧AB的长)为____. (结果保留\\(\\pi\\))","options":[],"answer":"","solution":"","stem_html":"<div>如图, 某游乐场的旋转木马旋转一周需240秒, 旋转半径是6米. 旋转时,一 木马某时刻在点A处，80秒后旋转到点B. 则该木马旋转的路径长(即弧AB的长)为____. (结果保留\\(\\pi\\))<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c4776514-9d6b-42a8-9e75-97d97333fe77/4995203021b9.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:11:08"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:11:08"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:11:08"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:11:28"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:11:33"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:11:33"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:11:33"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:12:05"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:12:05"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:13:03"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:13:03"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:14:24"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:14:24"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T10:14:24"}],"detail_url":"/questions/25474","edit_url":"/questions/25474/edit","json_url":"/api/questions/25474","recheck_url":"/api/questions/25474/recheck"},{"id":25468,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.775,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[2,3],"stem":"[小试1] 如图，点A, B, C在⊙O上,\\(\\angle ABC = 40^\\circ\\), 连接OA, OC. 若⊙ O的半径为3,则扇形AOC(阴影部分)的面积为( ) A. \\(2 _{3}\\pi\\) B. \\(\\pi\\) C. \\(4 _{3}\\pi\\) D. \\(2\\pi\\)","options":[{"label":"A","text":"2 _{3}\\pi"},{"label":"B","text":"\\pi"},{"label":"C","text":"4 _{3}\\pi"},{"label":"D","text":"2\\pi"}],"answer":"D","solution":"由题可得: ∵∠ABC = 40∘, ∴∠AOC = 2∠ABC = 80∘, 又⊙O的半径为3,所以扇形AOC(阴影部分)\\(80\\pi\\times 3^{2}\\)的面积为 =\\(2\\pi.\\)故选: D． 360","stem_html":"<div>[小试1]\n如图，点A, B, C在⊙O上,\\(\\angle ABC = 40^\\circ\\), 连接OA, OC. 若⊙ O的半径为3,则扇形AOC(阴影部分)的面积为( )<br>A. \\(2 _{3}\\pi\\)<br>B. \\(\\pi\\)<br>C. \\(4 _{3}\\pi\\)<br>D. \\(2\\pi\\)</div>","answer_html":"D","solution_html":"由题可得: ∵∠ABC = 40∘, ∴∠AOC = 2∠ABC = 80∘, 又⊙O的半径为3,所以扇形AOC(阴影部分)\\(80\\pi\\times 3^{2}\\)的面积为 =\\(2\\pi.\\)故选: D． 360","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:12:41"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:12:41"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:12:41"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:12:52"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:12:52"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T10:13:22"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:13:22"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T10:14:19"},{"type":"QUALITY_GATE","status":"FAIL","score":0.775,"created_at":"2026-09-26T10:14:19"}],"detail_url":"/questions/25468","edit_url":"/questions/25468/edit","json_url":"/api/questions/25468","recheck_url":"/api/questions/25468/recheck"},{"id":25473,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如果扇形弧长是9.42厘米, 圆心角是270∘, 那么这个扇形的面积是____平方厘米．","options":[],"answer":"","solution":"","stem_html":"<div>如果扇形弧长是9.42厘米, 圆心角是270∘, 那么这个扇形的面积是____平方厘米．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:08:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:08:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:08:17"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T10:08:37"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T10:09:11"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:09:11"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:09:11"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:09:27"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T10:09:27"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T10:11:06"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:11:06"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T10:12:31"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:12:31"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T10:12:31"}],"detail_url":"/questions/25473","edit_url":"/questions/25473/edit","json_url":"/api/questions/25473","recheck_url":"/api/questions/25473/recheck"},{"id":25470,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，点A在⊙O的直径CD的延长线上，点B在⊙O上，连接AB，BC. 若AB是⊙O的切线，AB = BC = 6，∠ABC = 120°，则图中阴影部分的面积是____．","options":[],"answer":"","solution":"","stem_html":"<div>如图，点A在⊙O的直径CD的延长线上，点B在⊙O上，连接AB，BC. 若AB是⊙O的切线，AB = BC = 6，∠ABC = 120°，则图中阴影部分的面积是____．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c8cf6e86-7b0e-4592-8735-25e01f320ce1/3dcdbd0b3ab9.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:08:18"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:08:18"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:08:18"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T10:08:45"}],"detail_url":"/questions/25470","edit_url":"/questions/25470/edit","json_url":"/api/questions/25470","recheck_url":"/api/questions/25470/recheck"},{"id":25467,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"360 已知某个扇形的弧长为圆心角为8,,  则这个扇形的面积为( ) ．16 32． ．64 ．16 A B C D","options":[],"answer":"","solution":"360  扇形的弧长为圆心角为8,，由l =\\(\\frac{nr}{180}\\)  l 8 得到r =\\(\\frac{180}{n} = \\frac{180}{360} = 4\\)    S扇形 =\\(\\frac{1}{2}\\)8 4 =16,故选 : ． A","stem_html":"<div>360 已知某个扇形的弧长为圆心角为8,,  则这个扇形的面积为( ) ．16 32． ．64 ．16 A B C D</div>","answer_html":"","solution_html":"360  扇形的弧长为圆心角为8,，由l =\\(\\frac{nr}{180}\\)  l 8 得到r =\\(\\frac{180}{n} = \\frac{180}{360} = 4\\)    S扇形 =\\(\\frac{1}{2}\\)8 4 =16,故选 : ． A","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:07:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:07:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:07:50"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T10:08:11"}],"detail_url":"/questions/25467","edit_url":"/questions/25467/edit","json_url":"/api/questions/25467","recheck_url":"/api/questions/25467/recheck"},{"id":25469,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.775,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"【小试2】 一个扇形的面积是\\(60\\pi{}cm^{2}\\)圆心角为150∘, 则此扇形的弧长是( ) A. \\(30\\pi{}cm\\) B. \\(10\\pi{}cm\\) C. \\(15\\pi{}cm\\) D. \\(20\\pi{}cm\\)","options":[{"label":"A","text":"30\\pi{}cm"},{"label":"B","text":"10\\pi{}cm"},{"label":"C","text":"15\\pi{}cm"},{"label":"D","text":"20\\pi{}cm"}],"answer":"B","solution":"\\(n\\pi{}r2 150\\pi{}r2\\)因为一个扇形的面积是\\(60\\pi{}cm^{2}\\)圆心角为150∘, S扇形= _{360}，\\(60\\pi = _{360}\\)解得r = 12, ∴ 此扇形的弧长为：\\(150\\pi\\times 12 = 10\\pi(cm)\\)故选: B． 180","stem_html":"<div>【小试2】 一个扇形的面积是\\(60\\pi{}cm^{2}\\)圆心角为150∘, 则此扇形的弧长是( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/544883f1-b0d6-42b2-9ac5-3afe6fef70da/08a98a5aa64c.png\" style=\"width:54.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(30\\pi{}cm\\)<br>B. \\(10\\pi{}cm\\)<br>C. \\(15\\pi{}cm\\)<br>D. \\(20\\pi{}cm\\)</div>","answer_html":"B","solution_html":"\\(n\\pi{}r2 150\\pi{}r2\\)因为一个扇形的面积是\\(60\\pi{}cm^{2}\\)圆心角为150∘, S扇形= _{360}，\\(60\\pi = _{360}\\)解得r = 12, ∴ 此扇形的弧长为：\\(150\\pi\\times 12 = 10\\pi(cm)\\)故选: B． 180","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:09:22"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:09:22"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:09:22"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T10:09:49"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:10:17"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:10:17"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:10:17"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T10:11:08"},{"type":"QUALITY_GATE","status":"FAIL","score":0.775,"created_at":"2026-09-26T10:11:08"}],"detail_url":"/questions/25469","edit_url":"/questions/25469/edit","json_url":"/api/questions/25469","recheck_url":"/api/questions/25469/recheck"},{"id":25451,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1470.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"扇形的面积：____________________","options":[],"answer":"S =\\(\\frac{1}{2}lr = \\frac{n\\pi r^{2}}{360}（n\\)是圆心角度数，r是半径，l是弧长）","solution":"根据《核心知识点》第4条，扇形面积公式有两种表达：一是用弧长l和半径r表示为S = 1/2 lr；二是用圆心角n（度数）、半径r表示为S =\\(n\\pi{}r^{2}/360\\)。这两个公式均直接来自提供的标准表述。","stem_html":"<div>扇形的面积：____________________</div>","answer_html":"S =\\(\\frac{1}{2}lr = \\frac{n\\pi r^{2}}{360}（n\\)是圆心角度数，r是半径，l是弧长）","solution_html":"根据《核心知识点》第4条，扇形面积公式有两种表达：一是用弧长l和半径r表示为S = 1/2 lr；二是用圆心角n（度数）、半径r表示为S =\\(n\\pi{}r^{2}/360\\)。这两个公式均直接来自提供的标准表述。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:03:04"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T10:03:04"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T10:03:04"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T10:03:19"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:03:54"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:03:54"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:03:54"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T10:03:56"},{"type":"QUALITY_GATE","status":"PASS","score":0.95,"created_at":"2026-09-26T10:03:56"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:04:11"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:04:11"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T10:04:23"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T10:04:24"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T10:04:24"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-09-26T10:04:24"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T10:04:44"}],"detail_url":"/questions/25451","edit_url":"/questions/25451/edit","json_url":"/api/questions/25451","recheck_url":"/api/questions/25451/recheck"},{"id":25438,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1465.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"(1)75∘的圆心角所对的弧长是\\(2.5\\pi{}cm\\)则此弧所在圆的半径是____cm; （1）一个扇形的弧长是\\(20\\pi\\)cm. 面积是\\(240\\pi\\)cm\\(^{2}\\), 则扇形的圆心角是____; （2）用一个圆心角为120∘, 半径为4的扇形作一个圆雉的侧面, 这个圆雉的底面圆的半为____．","options":[],"answer":"","solution":"","stem_html":"<div>(1)75∘的圆心角所对的弧长是\\(2.5\\pi{}cm\\)则此弧所在圆的半径是____cm;<br>（1）一个扇形的弧长是\\(20\\pi\\)cm. 面积是\\(240\\pi\\)cm\\(^{2}\\), 则扇形的圆心角是____;<br>（2）用一个圆心角为120∘, 半径为4的扇形作一个圆雉的侧面, 这个圆雉的底面圆的半为____．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:53:16"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:53:16"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:53:16"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:53:48"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:53:50"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:53:50"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:53:50"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:54:09"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T09:54:09"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T09:59:28"},{"type":"CRITIC","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:59:28"},{"type":"COHERENCE","status":"WARN","score":0.6,"created_at":"2026-09-26T10:02:21"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:02:21"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.8,"created_at":"2026-09-26T10:02:21"}],"detail_url":"/questions/25438","edit_url":"/questions/25438/edit","json_url":"/api/questions/25438","recheck_url":"/api/questions/25438/recheck"},{"id":25441,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1465.pdf","job_source":"人教版.zip","pages":[3,4],"stem":"6.某小区内的消防车道有一段弯道，如图，弯道的内外边缘均为圆弧，\\(\\widehat{AB}\\)，\\(\\widehat{CD}\\)所在圆的圆心为点O，点C，D分别在OA，OB上，已知消防车道半径OC = 12m，消防车道宽AC = 4m，\\(\\angle AOB = 120^{\\circ}\\)，则弯道外边缘\\(\\widehat{AB}\\)的长与内边缘\\(\\widehat{CD}\\)的长差为( ) A. \\(4\\pi\\) B. \\(8\\pi \\frac{_{3}m}{_{3}m}\\) C. \\(16\\pi\\) D. \\(32\\pi \\frac{_{3}m}{_{3}m}\\)","options":[{"label":"A","text":"4\\pi"},{"label":"B","text":"8\\pi \\frac{_{3}m}{_{3}m}"},{"label":"C","text":"16\\pi"},{"label":"D","text":"32\\pi \\frac{_{3}m}{_{3}m}"}],"answer":"B","solution":"由题意知，弯道内外边缘均为圆弧，圆心为点O。内边缘半径为OC=12m，外边缘半径为OA=OC+AC=12+4=16m。圆心角∠AOB=120°。 根据弧长公式：弧长 = (圆心角度数/360°)\\(\\times 2\\pi \\times\\)半径 外边缘弧长AB = (120/360)\\(\\times 2\\pi \\times 16 = (1/3) \\times 32\\pi = (32\\pi)/3\\)m 内边缘弧长CD = (120/360)\\(\\times 2\\pi \\times 12 = (1/3) \\times 24\\pi = (24\\pi)/3\\)m 两者之差 = (\\(32\\pi\\))/3 - (\\(24\\pi\\))/3 = (\\(8\\pi\\))/3 m 因此，弯道外边缘AB的长与内边缘CD的长差为 (\\(8\\pi\\))/3 m，对应选项B。","stem_html":"<div>6.某小区内的消防车道有一段弯道，如图，弯道的内外边缘均为圆弧，\\(\\widehat{AB}\\)，\\(\\widehat{CD}\\)所在圆的圆心为点O，点C，D分别在OA，OB上，已知消防车道半径OC = 12m，消防车道宽AC = 4m，\\(\\angle AOB = 120^{\\circ}\\)，则弯道外边缘\\(\\widehat{AB}\\)的长与内边缘\\(\\widehat{CD}\\)的长差为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/0838d2f3-4fb9-4a53-a976-130d08446b3e/d91151288a15.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(4\\pi\\)<br>B. \\(8\\pi \\frac{_{3}m}{_{3}m}\\)<br>C. \\(16\\pi\\)<br>D. \\(32\\pi \\frac{_{3}m}{_{3}m}\\)</div>","answer_html":"B","solution_html":"由题意知，弯道内外边缘均为圆弧，圆心为点O。内边缘半径为OC=12m，外边缘半径为OA=OC+AC=12+4=16m。圆心角∠AOB=120°。\n\n根据弧长公式：弧长 = (圆心角度数/360°)\\(\\times 2\\pi \\times\\)半径\n\n外边缘弧长AB = (120/360)\\(\\times 2\\pi \\times 16 = (1/3) \\times 32\\pi = (32\\pi)/3\\)m\n内边缘弧长CD = (120/360)\\(\\times 2\\pi \\times 12 = (1/3) \\times 24\\pi = (24\\pi)/3\\)m\n\n两者之差 = (\\(32\\pi\\))/3 - (\\(24\\pi\\))/3 = (\\(8\\pi\\))/3 m\n\n因此，弯道外边缘AB的长与内边缘CD的长差为 (\\(8\\pi\\))/3 m，对应选项B。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:57:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:57:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:57:50"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:58:07"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:00:23"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:00:23"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T10:00:23"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T10:00:27"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T10:00:27"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T10:00:59"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:00:59"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T10:01:51"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T10:01:51"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T10:01:51"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-09-26T10:01:51"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T10:02:00"}],"detail_url":"/questions/25441","edit_url":"/questions/25441/edit","json_url":"/api/questions/25441","recheck_url":"/api/questions/25441/recheck"},{"id":25436,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.912,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1465.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"⏜ 1.如图,点 A, B, C 在半径为 9 的 ⊙O 上，AB的长为\\(2\\pi\\)则∠ACB 的大小是____．","options":[],"answer":"","solution":"","stem_html":"<div>⏜ 1.如图,点 A, B, C 在半径为 9 的 ⊙O 上，AB的长为\\(2\\pi\\)则∠ACB 的大小是____．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:51:58"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:51:58"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:51:58"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T09:52:29"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T09:52:29"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:52:37"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:52:37"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:53:12"},{"type":"QUALITY_GATE","status":"FAIL","score":0.912,"created_at":"2026-09-26T09:53:12"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T09:57:17"},{"type":"CRITIC","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:57:17"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:58:09"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:58:09"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:58:09"}],"detail_url":"/questions/25436","edit_url":"/questions/25436/edit","json_url":"/api/questions/25436","recheck_url":"/api/questions/25436/recheck"},{"id":25435,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1465.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"【小试2】 （1）已知扇形的半径为4, 面积为4, 则该扇形的弧长为____. （2）若扇形的圆心角为\\(30^\\circ\\), 面积为\\(\\frac{\\pi}{3}\\)cm\\(^2\\), 则它的半径为____cm. （3）一个扇形的弧长是\\(10\\pi\\)cm, 面积是\\(60\\pi\\)cm\\(^{2}\\), 则此扇形的圆心角的度数是____．","options":[],"answer":"","solution":"","stem_html":"<div>【小试2】<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/60add775-86c3-435d-af72-a7e902db4509/206a15665d99.png\" style=\"width:54.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）已知扇形的半径为4, 面积为4, 则该扇形的弧长为____.<br>（2）若扇形的圆心角为\\(30^\\circ\\), 面积为\\(\\frac{\\pi}{3}\\)cm\\(^2\\), 则它的半径为____cm.<br>（3）一个扇形的弧长是\\(10\\pi\\)cm, 面积是\\(60\\pi\\)cm\\(^{2}\\), 则此扇形的圆心角的度数是____．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:52:30"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:52:30"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:52:30"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:52:40"}],"detail_url":"/questions/25435","edit_url":"/questions/25435/edit","json_url":"/api/questions/25435","recheck_url":"/api/questions/25435/recheck"},{"id":25439,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1465.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"一个扇形的弧长为\\(\\frac{4}{3}\\pi\\), 半径为6, 则此扇形的圆心角度数为____\\(^\\circ\\), 此扇形的面积为____．","options":[],"answer":"","solution":"","stem_html":"<div>一个扇形的弧长为\\(\\frac{4}{3}\\pi\\), 半径为6, 则此扇形的圆心角度数为____\\(^\\circ\\), 此扇形的面积为____．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:52:51"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:52:51"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:52:51"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:52:57"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:53:28"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:53:28"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:53:28"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:53:38"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T09:53:38"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:55:03"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:55:03"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:56:08"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:56:08"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T09:56:08"}],"detail_url":"/questions/25439","edit_url":"/questions/25439/edit","json_url":"/api/questions/25439","recheck_url":"/api/questions/25439/recheck"},{"id":25433,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1465.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"已知扇形的半径为6,面积为6,则扇形圆 如图,点,A B,C 在半径为9的 O 上， AB的长为2,则ACB 的度数是 ____. 心角的度数为( ) .30 .60 .90 .120 A B C D","options":[],"answer":"","solution":"【讲解】  扇形面积公式 : S =\\(\\frac{nr^{2}}{360}\\)代入S = 6, r = 6， 设AB所对的圆心角为n,由弧长公式 : 2= n9 ,解得n = 40，ACB =\\(\\frac{1}{2} 40=\\) 20. n\\(6^{2}\\) 180 6=,解得n = 30. 360","stem_html":"<div>已知扇形的半径为6,面积为6,则扇形圆 如图,点,A B,C 在半径为9的 O 上， AB的长为2,则ACB 的度数是 ____. 心角的度数为( ) .30 .60 .90 .120 A B C D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/7c1b05ad-b80c-48c9-b313-ee602f6e38ca/b80f26cc19e1.png\" style=\"width:140.0px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"【讲解】  扇形面积公式 : S =\\(\\frac{nr^{2}}{360}\\)代入S = 6, r = 6， 设AB所对的圆心角为n,由弧长公式 : 2= n9 ,解得n = 40，ACB =\\(\\frac{1}{2} 40=\\) 20. n\\(6^{2}\\) 180 6=,解得n = 30. 360","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:52:01"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:52:01"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:52:01"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:52:26"}],"detail_url":"/questions/25433","edit_url":"/questions/25433/edit","json_url":"/api/questions/25433","recheck_url":"/api/questions/25433/recheck"},{"id":25432,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1465.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"扇形的面积：____________________","options":[],"answer":"S =\\(\\frac{1}{2}lr = \\frac{n\\pi r^{2}}{360}\\)","solution":"根据扇形面积公式，扇形面积S等于弧长l与半径r乘积的一半，即S =\\(\\frac{1}{2}lr\\)；或者用圆心角n（度数）表示为S =\\(\\frac{n\\pi r^{2}}{360}\\)。","stem_html":"<div>扇形的面积：____________________</div>","answer_html":"S =\\(\\frac{1}{2}lr = \\frac{n\\pi r^{2}}{360}\\)","solution_html":"根据扇形面积公式，扇形面积S等于弧长l与半径r乘积的一半，即S =\\(\\frac{1}{2}lr\\)；或者用圆心角n（度数）表示为S =\\(\\frac{n\\pi r^{2}}{360}\\)。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:50:57"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:50:57"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:50:57"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:51:18"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:51:18"},{"type":"VISION","status":"PASS","score":0.8,"created_at":"2026-09-26T09:51:44"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:51:44"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T09:51:55"},{"type":"QUALITY_GATE","status":"PASS","score":0.925,"created_at":"2026-09-26T09:51:55"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:52:55"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:52:55"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:53:23"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:53:23"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T09:53:23"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-09-26T09:53:23"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T09:54:11"}],"detail_url":"/questions/25432","edit_url":"/questions/25432/edit","json_url":"/api/questions/25432","recheck_url":"/api/questions/25432/recheck"},{"id":25421,"job_id":3,"qa_status":"QUARANTINED","question_type":"knowledge","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":1.0,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1465.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"弧长公式：\\(l = \\frac{n\\pi r}{180^{\\circ}}\\)(n是扇形的圆心角，r是扇形半径) (n是扇形圆心角度数，l是弧长，r是扇形半径)","options":[],"answer":"","solution":"","stem_html":"<div>弧长公式：\\(l = \\frac{n\\pi r}{180^{\\circ}}\\)(n是扇形的圆心角，r是扇形半径) (n是扇形圆心角度数，l是弧长，r是扇形半径)</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-09-26T09:50:03"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:50:03"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T09:50:22"},{"type":"QUALITY_GATE","status":"FAIL","score":1.0,"created_at":"2026-09-26T09:50:22"}],"detail_url":"/questions/25421","edit_url":"/questions/25421/edit","json_url":"/api/questions/25421","recheck_url":"/api/questions/25421/recheck"},{"id":25417,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[4,5],"stem":"3.某小区内的消防车道有一段弯道，如图，弯道的内外边缘均为圆弧，\\(\\widehat{AB}\\)，\\(\\widehat{CD}\\)所在圆的圆心为点\\(O\\)，点\\(C\\)，\\(D\\)分别在\\(OA\\)，\\(OB\\)上，已知消防车道半径\\(OC = 12\\mathrm{m}\\)，消防车道宽\\(AC = 4\\mathrm{m}\\)，\\(\\angle AOB = 120^{\\circ}\\)，则弯道外边缘\\(\\widehat{AB}\\)的长与内边缘\\(\\widehat{CD}\\)的长差为( ) A. \\(4\\pi\\) B. \\(8\\pi \\frac{_{3}m}{_{3}m}\\) C. \\(16\\pi\\) D. \\(32\\pi _{3}m _{3}m\\)","options":[{"label":"A","text":"4\\pi"},{"label":"B","text":"8\\pi \\frac{_{3}m}{_{3}m}"},{"label":"C","text":"16\\pi"},{"label":"D","text":"32\\pi _{3}m _{3}m"}],"answer":"","solution":"","stem_html":"<div>3.某小区内的消防车道有一段弯道，如图，弯道的内外边缘均为圆弧，\\(\\widehat{AB}\\)，\\(\\widehat{CD}\\)所在圆的圆心为点\\(O\\)，点\\(C\\)，\\(D\\)分别在\\(OA\\)，\\(OB\\)上，已知消防车道半径\\(OC = 12\\mathrm{m}\\)，消防车道宽\\(AC = 4\\mathrm{m}\\)，\\(\\angle AOB = 120^{\\circ}\\)，则弯道外边缘\\(\\widehat{AB}\\)的长与内边缘\\(\\widehat{CD}\\)的长差为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/3b06511a-003f-4039-8643-a8b0e9c670ff/be87a48211a2.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(4\\pi\\)<br>B. \\(8\\pi \\frac{_{3}m}{_{3}m}\\)<br>C. \\(16\\pi\\)<br>D. \\(32\\pi _{3}m _{3}m\\)</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:48:45"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:48:45"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:48:45"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T09:49:04"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:49:24"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:49:24"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:49:24"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:49:28"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-09-26T09:49:28"}],"detail_url":"/questions/25417","edit_url":"/questions/25417/edit","json_url":"/api/questions/25417","recheck_url":"/api/questions/25417/recheck"},{"id":25418,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.913,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"一无盖纸杯如图1所示，经测量：杯口直径AB = 6cm，杯底直径CD = 4cm，杯壁AC = BD = 6cm，纸杯的侧面展开示意图为环形的一部分(如图2所示，忽略拼接部分)，则它所对的圆心角的度数n = ______.","options":[],"answer":"","solution":"","stem_html":"<div>一无盖纸杯如图1所示，经测量：杯口直径AB = 6cm，杯底直径CD = 4cm，杯壁AC = BD = 6cm，纸杯的侧面展开示意图为环形的一部分(如图2所示，忽略拼接部分)，则它所对的圆心角的度数n = ______.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/f2eb2f4f-e1b7-4c39-881d-91311c6a522b/098a9b2d8b81.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:41:19"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:41:19"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:41:19"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:41:49"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:44:45"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:44:45"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:44:45"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:44:53"},{"type":"QUALITY_GATE","status":"FAIL","score":0.913,"created_at":"2026-09-26T09:44:53"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T09:46:19"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T09:46:19"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:48:43"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-09-26T09:48:43"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:48:43"}],"detail_url":"/questions/25418","edit_url":"/questions/25418/edit","json_url":"/api/questions/25418","recheck_url":"/api/questions/25418/recheck"},{"id":25419,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.963,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，⊙O的半径为4. （1）求作它的内接正方形ABCD; （2）求正方形ABCD的边长.","options":[],"answer":"","solution":"","stem_html":"<div>如图，⊙O的半径为4.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/ed21d684-f7c6-4955-ab72-43c823527239/1d5380bf97e8.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）求作它的内接正方形ABCD;<br>（2）求正方形ABCD的边长.</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-09-26T09:40:18"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:40:18"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:40:18"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T09:40:40"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:40:57"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:40:57"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:40:57"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:41:08"},{"type":"QUALITY_GATE","status":"FAIL","score":0.963,"created_at":"2026-09-26T09:41:08"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:43:20"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:43:20"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:44:30"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:44:30"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T09:44:30"}],"detail_url":"/questions/25419","edit_url":"/questions/25419/edit","json_url":"/api/questions/25419","recheck_url":"/api/questions/25419/recheck"},{"id":25416,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.975,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"题目: ＂苏州之眼＂摩天轮是亚洲最大的水上摩天轮, 其示意图如图所示.该摩天轮的半径为60m, 摩天轮匀速旋转一圈用时30min. 某轿厢从点A出发，10min后到达点B, 此过程中该轿厢所经过的路径 (即弧AB)长度为____m. (结果保留\\(\\pi\\))","options":[],"answer":"","solution":"","stem_html":"<div>题目: ＂苏州之眼＂摩天轮是亚洲最大的水上摩天轮, 其示意图如图所示.该摩天轮的半径为60m, 摩天轮匀速旋转一圈用时30min. 某轿厢从点A出发，10min后到达点B, 此过程中该轿厢所经过的路径 (即弧AB)长度为____m. (结果保留\\(\\pi\\))<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/1cb64d95-f658-4a39-8586-6cabf624e4df/a79bbd7eda05.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:38:54"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:38:54"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:38:54"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T09:39:19"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:39:19"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:39:19"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:39:19"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T09:39:27"},{"type":"QUALITY_GATE","status":"FAIL","score":0.975,"created_at":"2026-09-26T09:39:27"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:40:27"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:40:27"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:43:06"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:43:06"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T09:43:06"}],"detail_url":"/questions/25416","edit_url":"/questions/25416/edit","json_url":"/api/questions/25416","recheck_url":"/api/questions/25416/recheck"},{"id":25410,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"当两个弧有相同的圆心角时，它们的弧长差可","options":[],"answer":"以\\(\\frac{n}{180}\\)表示","solution":"根据弧长公式 l =\\(\\frac{nr}{180}\\)，当两个弧的圆心角 n 相同时，弧长差\\(l_{1}\\)-\\(l_{2}\\)=\\(\\frac{n}{180}(r_{1} - r_{2})\\)，其中\\(\\frac{n}{180}\\)是比例系数。","stem_html":"<div>当两个弧有相同的圆心角时，它们的弧长差可</div>","answer_html":"以\\(\\frac{n}{180}\\)表示","solution_html":"根据弧长公式 l =\\(\\frac{nr}{180}\\)，当两个弧的圆心角 n 相同时，弧长差\\(l_{1}\\)-\\(l_{2}\\)=\\(\\frac{n}{180}(r_{1} - r_{2})\\)，其中\\(\\frac{n}{180}\\)是比例系数。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:38:06"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:38:06"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:38:06"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T09:38:22"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T09:38:22"},{"type":"VISION","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:38:31"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:38:31"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T09:39:42"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T09:39:42"}],"detail_url":"/questions/25410","edit_url":"/questions/25410/edit","json_url":"/api/questions/25410","recheck_url":"/api/questions/25410/recheck"},{"id":25408,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"当两个弧有相同的圆心角时，它们的弧长差可","options":[],"answer":"表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)\\)","solution":"根据弧长公式 l =\\(\\frac{nr}{180}\\)，当两个弧的圆心角 n 相同时，弧长差 l₁ - l₂ =\\(\\frac{n r₁}{180} - \\frac{n r₂}{180} = \\frac{n}{180}(r₁ - r₂)\\)。","stem_html":"<div>当两个弧有相同的圆心角时，它们的弧长差可</div>","answer_html":"表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)\\)","solution_html":"根据弧长公式 l =\\(\\frac{nr}{180}\\)，当两个弧的圆心角 n 相同时，弧长差 l₁ - l₂ =\\(\\frac{n r₁}{180} - \\frac{n r₂}{180} = \\frac{n}{180}(r₁ - r₂)\\)。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:37:33"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:37:33"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:37:33"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:38:00"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:38:00"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:38:24"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:38:24"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:38:54"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:38:54"}],"detail_url":"/questions/25408","edit_url":"/questions/25408/edit","json_url":"/api/questions/25408","recheck_url":"/api/questions/25408/recheck"},{"id":25402,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.837,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"当两个弧有相同的圆心角时，它们的弧长差可","options":[],"answer":"以表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)（n\\)是扇形的圆心角，r是扇形半径）","solution":"根据弧长公式 l =\\(\\frac{nr}{180}°\\)，当两个弧有相同的圆心角 n 时，它们的弧长差可表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)\\)。","stem_html":"<div>当两个弧有相同的圆心角时，它们的弧长差可</div>","answer_html":"以表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)（n\\)是扇形的圆心角，r是扇形半径）","solution_html":"根据弧长公式 l =\\(\\frac{nr}{180}°\\)，当两个弧有相同的圆心角 n 时，它们的弧长差可表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)\\)。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:36:23"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:23"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:36:23"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:39"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:39"},{"type":"VISION","status":"FAIL","score":0.5,"created_at":"2026-09-26T09:37:02"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:37:02"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:38:35"},{"type":"QUALITY_GATE","status":"FAIL","score":0.837,"created_at":"2026-09-26T09:38:35"}],"detail_url":"/questions/25402","edit_url":"/questions/25402/edit","json_url":"/api/questions/25402","recheck_url":"/api/questions/25402/recheck"},{"id":25404,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.912,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"当两个弧有相同的圆心角时，它们的弧长差可","options":[],"answer":"以表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)\\)","solution":"根据弧长公式 l =\\(\\frac{nr}{180}\\)，当两个弧的圆心角 n 相同时，弧长差为\\(\\frac{n}{180}(r₁ - r₂)\\)。","stem_html":"<div>当两个弧有相同的圆心角时，它们的弧长差可</div>","answer_html":"以表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)\\)","solution_html":"根据弧长公式 l =\\(\\frac{nr}{180}\\)，当两个弧的圆心角 n 相同时，弧长差为\\(\\frac{n}{180}(r₁ - r₂)\\)。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-09-26T09:36:25"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:25"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:36:25"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:38"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:37:38"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:37:38"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:37:54"},{"type":"QUALITY_GATE","status":"FAIL","score":0.912,"created_at":"2026-09-26T09:37:54"}],"detail_url":"/questions/25404","edit_url":"/questions/25404/edit","json_url":"/api/questions/25404","recheck_url":"/api/questions/25404/recheck"},{"id":25406,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.838,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1460.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"当两个弧有相同的圆心角时，它们的弧长差可","options":[],"answer":"以表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)\\)","solution":"根据弧长公式 l =\\(\\frac{nr}{180}\\)，当两个弧的圆心角 n 相同时，弧长差为各自弧长公式的差值，即\\(\\frac{n r_{1}}{180} - \\frac{n r_{2}}{180} = \\frac{n}{180}(r_{1} - r_{2})\\)。","stem_html":"<div>当两个弧有相同的圆心角时，它们的弧长差可</div>","answer_html":"以表示为：l₁ - l₂ =\\(\\frac{n}{180}(r₁ - r₂)\\)","solution_html":"根据弧长公式 l =\\(\\frac{nr}{180}\\)，当两个弧的圆心角 n 相同时，弧长差为各自弧长公式的差值，即\\(\\frac{n r_{1}}{180} - \\frac{n r_{2}}{180} = \\frac{n}{180}(r_{1} - r_{2})\\)。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-09-26T09:36:25"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:25"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:36:25"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:40"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:36:40"},{"type":"VISION","status":"FAIL","score":0.5,"created_at":"2026-09-26T09:37:36"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:37:36"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:37:52"},{"type":"QUALITY_GATE","status":"FAIL","score":0.838,"created_at":"2026-09-26T09:37:52"}],"detail_url":"/questions/25406","edit_url":"/questions/25406/edit","json_url":"/api/questions/25406","recheck_url":"/api/questions/25406/recheck"},{"id":25396,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.912,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1455.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"历史上，对于圆周率\\(\\pi\\)的研究是古代数学一个经久不衰的话题，如我 国魏晋时期的数学家刘徽首创 \"割圆术 \"，利用圆的内接正多边形 来确定圆周率，可见正多边形与圆联系非常紧密！ （1）如图，请在 ⊙ O中，作一个圆内接正六边形ABCDEF．(要求 :尺规 作图，不写作法，没有作图痕迹不给分) （2）若正六边形边长为3，求该正六边形的边心距．","options":[],"answer":"3√3","solution":"(1)见解析; (2). 2    (1)如图，六边形ABCDEF即为所求；证明：由作图可得AB = BC = CD=       DE = EF = FA， ∴ AB=BC =CD=DE =EF =FA, BDF = AEC = BED=    CAE = DAF = ACE,∴ ∠FAB= ∠ABC = ∠BCD= ∠CDE = ∠DEF= ∠EFA, ∴六边形ABCDEF是圆内接正六边形； (2)连接OA,OB，过点O作OH ⊥ AB于点H． ∵ 六边形ABCDEF是圆内接正六 360∘ 边形， ∴ ∠AOB= = 60∘, OA = OB，∴△OAB是等边三角形，∴OA = OB= 6 3√3 AB= 3,∵ OH ⊥ AB,∴ BH =\\(\\frac{1}{2}\\)AB=\\(\\frac{3}{2}\\)∴OH=\\(\\sqrt{OB^{2}}\\)−\\(BH^{2}\\)=,即正六 2 3√3 边形的边心距为. 2","stem_html":"<div>历史上，对于圆周率\\(\\pi\\)的研究是古代数学一个经久不衰的话题，如我 国魏晋时期的数学家刘徽首创 \"割圆术 \"，利用圆的内接正多边形 来确定圆周率，可见正多边形与圆联系非常紧密！<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/071e6a84-d95c-4960-a8e9-fced03b3503d/1fa5d9a6df1d.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）如图，请在 ⊙ O中，作一个圆内接正六边形ABCDEF．(要求 :尺规 作图，不写作法，没有作图痕迹不给分)<br>（2）若正六边形边长为3，求该正六边形的边心距．</div>","answer_html":"3√3","solution_html":"(1)见解析; (2). 2    (1)如图，六边形ABCDEF即为所求；证明：由作图可得AB = BC = CD=       DE = EF = FA， ∴ AB=BC =CD=DE =EF =FA, BDF = AEC = BED=    CAE = DAF = ACE,∴ ∠FAB= ∠ABC = ∠BCD= ∠CDE = ∠DEF= ∠EFA, ∴六边形ABCDEF是圆内接正六边形； (2)连接OA,OB，过点O作OH ⊥ AB于点H． ∵ 六边形ABCDEF是圆内接正六 360∘ 边形， ∴ ∠AOB= = 60∘, OA = OB，∴△OAB是等边三角形，∴OA = OB= 6 3√3 AB= 3,∵ OH ⊥ AB,∴ BH =\\(\\frac{1}{2}\\)AB=\\(\\frac{3}{2}\\)∴OH=\\(\\sqrt{OB^{2}}\\)−\\(BH^{2}\\)=,即正六 2 3√3 边形的边心距为. 2","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:31:54"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:31:54"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:31:54"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:32:31"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T09:34:18"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:34:18"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:34:18"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:34:41"},{"type":"QUALITY_GATE","status":"FAIL","score":0.912,"created_at":"2026-09-26T09:34:41"}],"detail_url":"/questions/25396","edit_url":"/questions/25396/edit","json_url":"/api/questions/25396","recheck_url":"/api/questions/25396/recheck"},{"id":25394,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1455.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，正五边形$ABCDE$中，点$F,G$分别是$BC,CD$的中点，\\(AF\\)与\\(BG\\)相交于点\\(H\\)． (1) 求证：\\(\\triangle ABF \\cong \\triangle BCG\\)； (2) 求\\(\\angle AHG\\)的度数．","options":[],"answer":"(1)见解析(2)∠AHG = 108°","solution":"(1)∵ 五边形ABCDE是正五边形,∴ ∠ABF = ∠BCG,AB=BC =CD,∵ 点 F ,G分别是BC,CD的中点,∴ BF =\\(\\frac{1}{2}\\)BC,CG=\\(\\frac{1}{2}\\)CD,∴ BF =CG,在 △ ABF在 ⎧⎪ AB=BC △ BCG中，⎨ ∠ABF = ∠BCG,∴△ ABF ≅△ BCG(SAS) ⎩⎪ BF =CG (2)∵△ ABF ≅△ BCG,∴ ∠BAF = ∠CBG，根据多边形内角和公式，可得 180∘\\(\\times (5 −2)\\)∠ABC = = 108∘，∴∠AHG = ∠ABH + ∠BAF= ∠ABH+∠CBG = ∠ABC= 108∘． 5","stem_html":"<div>如图，正五边形$ABCDE$中，点$F,G$分别是$BC,CD$的中点，\\(AF\\)与\\(BG\\)相交于点\\(H\\)．\n(1) 求证：\\(\\triangle ABF \\cong \\triangle BCG\\)；\n(2) 求\\(\\angle AHG\\)的度数．</div>","answer_html":"(1)见解析(2)∠AHG = 108°","solution_html":"(1)∵ 五边形ABCDE是正五边形,∴ ∠ABF = ∠BCG,AB=BC =CD,∵ 点 F ,G分别是BC,CD的中点,∴ BF =\\(\\frac{1}{2}\\)BC,CG=\\(\\frac{1}{2}\\)CD,∴ BF =CG,在 △ ABF在 ⎧⎪ AB=BC △ BCG中，⎨ ∠ABF = ∠BCG,∴△ ABF ≅△ BCG(SAS) ⎩⎪ BF =CG (2)∵△ ABF ≅△ BCG,∴ ∠BAF = ∠CBG，根据多边形内角和公式，可得 180∘\\(\\times (5 −2)\\)∠ABC = = 108∘，∴∠AHG = ∠ABH + ∠BAF= ∠ABH+∠CBG = ∠ABC= 108∘． 5","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:28:03"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:28:03"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:28:03"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:28:47"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T09:29:16"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T09:29:16"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:29:16"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:30:05"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T09:30:05"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T09:30:44"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:30:44"},{"type":"COHERENCE","status":"FAIL","score":0.85,"created_at":"2026-09-26T09:33:17"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-09-26T09:33:17"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:33:17"}],"detail_url":"/questions/25394","edit_url":"/questions/25394/edit","json_url":"/api/questions/25394","recheck_url":"/api/questions/25394/recheck"},{"id":25392,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1455.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，四边形$ABCD 是\\(odot O\\)的内接四边形，\\(CD\\)是圆内接十边形的一条边，\\(angle ACD = 32^circ\\)．若\\(odot O\\)的半径为5，则\\(widehatAC\\)的长为 ______．","options":[],"answer":"\\(\\frac{25}{9} \\pi\\)","solution":"连接OA, OD, OC, ∵∠ACD = 32∘, ∴∠AOD = 64∘; ∵CD是圆内接十边形的一  360∘ 条边,∴ ∠COD= = 36∘, ∴∠AOC= ∠AOD + ∠COD = 100∘, ∴ AC的长 10 100∘\\(\\times \\pi \\times 5 25\\pi =\\)故答案为：\\(\\frac{25}{9} \\pi\\). 为： 180∘ 9","stem_html":"<div>如图，四边形$ABCD<span class=\"formula-fallback\">是\\(odot O\\)的内接四边形，\\(CD\\)是圆内接十边形的一条边，\\(angle ACD = 32^circ\\)．若\\(odot O\\)的半径为5，则\\(widehatAC\\)的长为 ______．</span><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/d20b6a8b-51c4-43ca-959f-8dd6b834f0eb/0240012b7d82.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"\\(\\frac{25}{9} \\pi\\)","solution_html":"连接OA, OD, OC, ∵∠ACD = 32∘, ∴∠AOD = 64∘; ∵CD是圆内接十边形的一  360∘ 条边,∴ ∠COD= = 36∘, ∴∠AOC= ∠AOD + ∠COD = 100∘, ∴ AC的长 10 100∘\\(\\times \\pi \\times 5 25\\pi =\\)故答案为：\\(\\frac{25}{9} \\pi\\). 为： 180∘ 9","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:26:05"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:26:05"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:26:05"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:26:38"}],"detail_url":"/questions/25392","edit_url":"/questions/25392/edit","json_url":"/api/questions/25392","recheck_url":"/api/questions/25392/recheck"},{"id":25391,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1455.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图， ⊙ O的内接正六边形为正六边形ABCDEF, ⊙O的半径为6，则B 的长为 ____． F","options":[],"answer":"6√3","solution":"如图，连接OA,OB,OF,OA交BF于M,∵ ⊙O的内接正六边形为正六边形 360∘ ABCDEF,∴ ∠AOB= = 60∘, ∠AFB =\\(\\frac{1}{2}\\)∠AOB = 30∘, ∵OA = OB，所 6 以△BOA是等边三角形, ∴AB = OA = OB = 6, ∠OAB = 60∘, ∴AM=\\(\\frac{1}{2}\\)⋅ A B = 3, 在Rt △AMB中MB =\\(\\sqrt{AB^{2}}\\)−\\(AM^{2}\\)=\\(\\sqrt{6^{2}}\\)−\\(3^{2}\\)= 3√3; 同理证得△FO A是等边三角形，AF =OA=OF = 6，∠ABF =\\(\\frac{1}{2}\\)∠AOF= 30∘, ∠OAF= 60∘，在Rt △AMF中MF=\\(\\sqrt{AF^{2}}\\)−\\(AM^{2}\\)=\\(\\sqrt{6^{2}}\\)−\\(3^{2}\\)= 3√3；BF= MF+ MB = 6√3. 故答案为6√3．\\(\\frac{25}{9} \\pi\\)","stem_html":"<div>如图， ⊙ O的内接正六边形为正六边形ABCDEF, ⊙O的半径为6，则B 的长为 ____． F<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/8b7dc6a4-1881-47ad-bbd5-c663a8672c69/d9787d1adf76.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"6√3","solution_html":"如图，连接OA,OB,OF,OA交BF于M,∵ ⊙O的内接正六边形为正六边形 360∘ ABCDEF,∴ ∠AOB= = 60∘, ∠AFB =\\(\\frac{1}{2}\\)∠AOB = 30∘, ∵OA = OB，所 6 以△BOA是等边三角形, ∴AB = OA = OB = 6, ∠OAB = 60∘, ∴AM=\\(\\frac{1}{2}\\)⋅ A B = 3, 在Rt △AMB中MB =\\(\\sqrt{AB^{2}}\\)−\\(AM^{2}\\)=\\(\\sqrt{6^{2}}\\)−\\(3^{2}\\)= 3√3; 同理证得△FO A是等边三角形，AF =OA=OF = 6，∠ABF =\\(\\frac{1}{2}\\)∠AOF= 30∘, ∠OAF= 60∘，在Rt △AMF中MF=\\(\\sqrt{AF^{2}}\\)−\\(AM^{2}\\)=\\(\\sqrt{6^{2}}\\)−\\(3^{2}\\)= 3√3；BF= MF+ MB = 6√3. 故答案为6√3．\\(\\frac{25}{9} \\pi\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:24:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:24:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:24:17"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:25:08"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T09:25:29"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T09:25:29"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:25:29"}],"detail_url":"/questions/25391","edit_url":"/questions/25391/edit","json_url":"/api/questions/25391","recheck_url":"/api/questions/25391/recheck"},{"id":25388,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1455.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图,AC是 ⊙ O的内接正四边形的一边,点B在弧AC上,且BC是 ⊙ O的内接 正六边形的一边. 若AB是⊙O的内接正n边形的一边, 则n的值为( ) A. \\(\\frac{6}{8}\\) B. C. 10 D. 12","options":[{"label":"A","text":"\\frac{6}{8}"},{"label":"B","text":""},{"label":"C","text":"10"},{"label":"D","text":"12"}],"answer":"D","solution":"连接AO, BO, CO. 因为AC是⊙O内接正四边形的一边，所以圆心角∠AOC = 360°÷4 = 90°. 因为BC是⊙O内接正六边形的一边，所以圆心角∠BOC = 360°÷6 = 60°. 点B在弧AC上，且BC为正六边形边，说明B位于A、C之间靠近C的位置，因此弧AB = 弧AC − 弧BC，对应的圆心角∠AOB = ∠AOC − ∠BOC = 90° − 60° = 30°. 由于AB是⊙O内接正n边形的一边，则360°能被∠AOB整除，即n = 360°÷30° = 12. 故选D.","stem_html":"<div>如图,AC是 ⊙ O的内接正四边形的一边,点B在弧AC上,且BC是 ⊙ O的内接 正六边形的一边. 若AB是⊙O的内接正n边形的一边, 则n的值为(      )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/3bd07b5f-40ae-47e3-b995-cc619ed732e8/219d6abc5032.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(\\frac{6}{8}\\)<br>B. <br>C. 10<br>D. 12</div>","answer_html":"D","solution_html":"连接AO, BO, CO. 因为AC是⊙O内接正四边形的一边，所以圆心角∠AOC = 360°÷4 = 90°. 因为BC是⊙O内接正六边形的一边，所以圆心角∠BOC = 360°÷6 = 60°. 点B在弧AC上，且BC为正六边形边，说明B位于A、C之间靠近C的位置，因此弧AB = 弧AC − 弧BC，对应的圆心角∠AOB = ∠AOC − ∠BOC = 90° − 60° = 30°. 由于AB是⊙O内接正n边形的一边，则360°能被∠AOB整除，即n = 360°÷30° = 12. 故选D.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:21:01"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:21:01"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:21:01"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T09:21:30"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T09:21:43"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T09:21:43"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:21:43"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:23:23"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:23:23"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:25:13"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:25:13"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T09:26:51"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:26:51"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":0.95,"created_at":"2026-09-26T09:26:51"},{"type":"AUTO_REPAIR","status":"PASS","score":0.95,"created_at":"2026-09-26T09:26:51"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T09:27:17"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/25388","edit_url":"/questions/25388/edit","json_url":"/api/questions/25388","recheck_url":"/api/questions/25388/recheck"},{"id":25386,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.913,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1455.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"如图，点A,B,C,D为一个正多边形的部分顶点，点O为正多边形的中心，若∠AOD = 120∘，则这个正多边形的边数为( ) A. \\(\\frac{6}{9}\\) B. C. 10 D. 12","options":[{"label":"A","text":"\\frac{6}{9}"},{"label":"B","text":""},{"label":"C","text":"10"},{"label":"D","text":"12"}],"answer":"B","solution":"如图：连接OC、OB，∵点O为正多边形的中心，∠AOD = 120∘, ∴∠AOB=\\(\\frac{1}{3}\\)∠AOD = 40∘, ∴360∘÷ 40∘= 9, ∴这个正多边形的边数为9，即选项B符合题意.","stem_html":"<div>如图，点A,B,C,D为一个正多边形的部分顶点，点O为正多边形的中心，若∠AOD = 120∘，则这个正多边形的边数为(      )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/f09483e2-1cdd-4823-b0f5-d8bc3e77bd12/e432719839e1.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(\\frac{6}{9}\\)<br>B. <br>C. 10<br>D. 12</div>","answer_html":"B","solution_html":"如图：连接OC、OB，∵点O为正多边形的中心，∠AOD = 120∘, ∴∠AOB=\\(\\frac{1}{3}\\)∠AOD = 40∘, ∴360∘÷ 40∘= 9, ∴这个正多边形的边数为9，即选项B符合题意.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:19:20"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:19:20"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:19:20"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:19:45"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:19:47"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:19:47"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:19:47"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:22:48"},{"type":"QUALITY_GATE","status":"FAIL","score":0.913,"created_at":"2026-09-26T09:22:48"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T09:24:22"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T09:24:22"},{"type":"COHERENCE","status":"FAIL","score":0.85,"created_at":"2026-09-26T09:25:53"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:25:53"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:25:53"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/25386","edit_url":"/questions/25386/edit","json_url":"/api/questions/25386","recheck_url":"/api/questions/25386/recheck"},{"id":25384,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1455.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"我国古代数学家刘徽在《九章算术注》中提到了＂割圆术＂，其核心 是通过圆内接正多边形的面积逐步逼近圆的面积,以实现对\\(\\pi\\)的近似 估算．如图， ⊙ O的半径为1，则圆的面积为\\(\\pi\\)，若将其内接正十二边 形的面积作为⊙O面积的近似值．据此，可得\\(\\pi\\)的估计值为( ) A. √10 B. 3.14 C. 3.13 D. 3","options":[{"label":"A","text":"√10"},{"label":"B","text":"3.14"},{"label":"C","text":"3.13"},{"label":"D","text":"3"}],"answer":"D","solution":"如图，设AB是⊙O正十二边形的一边，过点A作AM⊥OB，垂足为M。所以∠AOB = 360°÷12 = 30°，在Rt△OAM中，OA = 1，∠AOM = 30°，∴ AM =\\(\\frac{1}{2}OA = \\frac{1}{2}\\)，∴\\(S_{△AOB}\\)=\\(\\frac{1}{2}OB·AM = \\frac{1}{4}\\)，∴ 正十二边形的面积为\\(\\frac{1}{4}\\times 12 = 3\\)，即⊙O的面积为3，此时\\(\\pi≈3．\\)故选D．","stem_html":"<div>我国古代数学家刘徽在《九章算术注》中提到了＂割圆术＂，其核心 是通过圆内接正多边形的面积逐步逼近圆的面积,以实现对\\(\\pi\\)的近似 估算．如图， ⊙ O的半径为1，则圆的面积为\\(\\pi\\)，若将其内接正十二边 形的面积作为⊙O面积的近似值．据此，可得\\(\\pi\\)的估计值为(      )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/30960c4b-5f04-40d8-9a1b-fa1b8f727895/066759ac3c55.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. √10<br>B. 3.14<br>C. 3.13<br>D. 3</div>","answer_html":"D","solution_html":"如图，设AB是⊙O正十二边形的一边，过点A作AM⊥OB，垂足为M。所以∠AOB = 360°÷12 = 30°，在Rt△OAM中，OA = 1，∠AOM = 30°，∴ AM =\\(\\frac{1}{2}OA = \\frac{1}{2}\\)，∴\\(S_{△AOB}\\)=\\(\\frac{1}{2}OB·AM = \\frac{1}{4}\\)，∴ 正十二边形的面积为\\(\\frac{1}{4}\\times 12 = 3\\)，即⊙O的面积为3，此时\\(\\pi≈3．\\)故选D．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:18:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:18:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:18:34"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:19:07"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T09:19:39"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:19:39"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:19:39"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:22:28"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T09:22:28"}],"detail_url":"/questions/25384","edit_url":"/questions/25384/edit","json_url":"/api/questions/25384","recheck_url":"/api/questions/25384/recheck"},{"id":25375,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1450.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"若扇形OAB的半径为6,AOB =120,则 如图已知,O 的半径为1cm,求作 O 的内接正八边形. AB的长为( ) .2 .3 .4 .6 A B C D","options":[],"answer":"","solution":"【讲解】  弧长公式 : l =\\(\\frac{nr}{180}\\)代入n =120, r = 6,  l =\\(\\frac{120}{180} =\\) 64. 故选. C :\\(\\frac{如图}{(1)}\\)AC，使AC = 2cm；\\(\\frac{作直径}{AC} \\frac{(2)}{(3)}\\)作 的垂直平分线交  O 于点,；\\(\\frac{BD}{AD}\\)连接AD，作AD的垂直平分线交 于点M； (4)用同样的方法分别作出AB, BC,C D 的中点E, F,G； (5)依次连接各分点则多边形.AEBFC DM G 即所求作的 O 的内接正八边形．","stem_html":"<div>若扇形OAB的半径为6,AOB =120,则 如图已知,O 的半径为1cm,求作 O 的内接正八边形. AB的长为( ) .2 .3 .4 .6 A B C D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/1582a4ad-ba6b-4cb8-8b10-fc4591d55506/51b9a90dd98f.png\" style=\"width:190.0px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"【讲解】  弧长公式 : l =\\(\\frac{nr}{180}\\)代入n =120, r = 6,  l =\\(\\frac{120}{180} =\\) 64. 故选. C :\\(\\frac{如图}{(1)}\\)AC，使AC = 2cm；\\(\\frac{作直径}{AC} \\frac{(2)}{(3)}\\)作 的垂直平分线交  O 于点,；\\(\\frac{BD}{AD}\\)连接AD，作AD的垂直平分线交 于点M； (4)用同样的方法分别作出AB, BC,C D 的中点E, F,G； (5)依次连接各分点则多边形.AEBFC DM G 即所求作的 O 的内接正八边形．","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:13:04"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:13:04"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:13:04"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T09:13:35"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:14:53"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:14:53"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:14:53"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T09:15:08"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T09:15:08"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:15:33"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:15:33"},{"type":"COHERENCE","status":"FAIL","score":0.85,"created_at":"2026-09-26T09:15:48"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:15:48"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T09:15:48"}],"detail_url":"/questions/25375","edit_url":"/questions/25375/edit","json_url":"/api/questions/25375","recheck_url":"/api/questions/25375/recheck"},{"id":25383,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1450.pdf","job_source":"人教版.zip","pages":[6,6],"stem":"如图，在正五边形ABCDE中，F是边CD的中点，则∠1的度数为_____.","options":[],"answer":"","solution":"","stem_html":"<div>如图，在正五边形ABCDE中，F是边CD的中点，则∠1的度数为_____.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/010433f6-8ae9-4b62-b57f-f5df43ec720d/02fa82120dce.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:10:32"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:10:32"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:10:32"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T09:10:54"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T09:12:25"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:12:25"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:12:25"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:12:30"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:12:31"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T09:14:43"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:14:43"},{"type":"COHERENCE","status":"FAIL","score":0.85,"created_at":"2026-09-26T09:15:35"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:15:35"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:15:35"}],"detail_url":"/questions/25383","edit_url":"/questions/25383/edit","json_url":"/api/questions/25383","recheck_url":"/api/questions/25383/recheck"},{"id":25381,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.913,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1450.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，已知⊙O的半径为1, AB是⊙O的弦，若AB =\\(\\sqrt{2}\\)，则劣弧AB的长为( ) A. \\(2\\pi\\) B. \\(\\pi\\) C. \\(\\pi\\) D. \\(\\pi \\frac{2}{4}\\)","options":[{"label":"A","text":"2\\pi"},{"label":"B","text":"\\pi"},{"label":"C","text":"\\pi"},{"label":"D","text":"\\pi \\frac{2}{4}"}],"answer":"","solution":"","stem_html":"<div>如图，已知⊙O的半径为1, AB是⊙O的弦，若AB =\\(\\sqrt{2}\\)，则劣弧AB的长为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/4aa8d27f-085c-4cb7-9a17-3ac49684a99e/c41819bfa8b5.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(2\\pi\\)<br>B. \\(\\pi\\)<br>C. \\(\\pi\\)<br>D. \\(\\pi \\frac{2}{4}\\)</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:12:14"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:12:14"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:12:14"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:12:32"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:13:01"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:13:01"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:13:01"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:13:37"},{"type":"QUALITY_GATE","status":"FAIL","score":0.913,"created_at":"2026-09-26T09:13:37"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T09:14:10"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:14:10"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:15:06"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:15:06"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T09:15:06"}],"detail_url":"/questions/25381","edit_url":"/questions/25381/edit","json_url":"/api/questions/25381","recheck_url":"/api/questions/25381/recheck"},{"id":25382,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1450.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"我国魏晋时期数学家刘徽在《九章算术注》中提到著名的\"割圆术\"，即 利用圆的内接正多边形逼近圆的方法来近似估算，指出\"割之弥细，所失弥少. 割之又割，以至于不可割，则与圆周合体，而无所失 矣\"．\"割圆术\"孕育了微积分思想，他用这种思想得到了圆周率\\(\\pi\\)的近似值为3.1416, 如图, 若⊙ O的半径为1．(在求圆内接正多边形面积时，通过分割成三角形，利用特殊角解决) （1）求圆内接正六边形面积． （2）圆内接正八边形的面积为______. （3）运用＂割圆术＂，用圆内接正十二边形近似估计⊙O的面积，可得圆内接正十二边形面积是 ______，可得\\(\\pi\\)的估计值为______．","options":[],"answer":"","solution":"","stem_html":"<div>我国魏晋时期数学家刘徽在《九章算术注》中提到著名的\"割圆术\"，即 利用圆的内接正多边形逼近圆的方法来近似估算，指出\"割之弥细，所失弥少. 割之又割，以至于不可割，则与圆周合体，而无所失 矣\"．\"割圆术\"孕育了微积分思想，他用这种思想得到了圆周率\\(\\pi\\)的近似值为3.1416, 如图, 若⊙ O的半径为1．(在求圆内接正多边形面积时，通过分割成三角形，利用特殊角解决)<br>（1）求圆内接正六边形面积．<br>（2）圆内接正八边形的面积为______.<br>（3）运用＂割圆术＂，用圆内接正十二边形近似估计⊙O的面积，可得圆内接正十二边形面积是 ______，可得\\(\\pi\\)的估计值为______．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:10:31"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:10:31"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:10:31"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:12:51"}],"detail_url":"/questions/25382","edit_url":"/questions/25382/edit","json_url":"/api/questions/25382","recheck_url":"/api/questions/25382/recheck"},{"id":25379,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1450.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图1，有一个亭子，它的地基是半径为4米的正六边形． （1）请在图2中利用尺规作出正六边形ABCDEF(不写作法, 保留作图痕迹)； （2）求地基的面积(答案保留根号).","options":[],"answer":"","solution":"","stem_html":"<div>如图1，有一个亭子，它的地基是半径为4米的正六边形．<br>（1）请在图2中利用尺规作出正六边形ABCDEF(不写作法, 保留作图痕迹)；<br>（2）求地基的面积(答案保留根号).</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:09:56"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:09:56"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:09:56"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T09:10:14"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T09:11:23"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T09:11:23"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T09:11:23"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:11:34"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:11:34"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:12:27"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:12:27"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:13:58"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:13:58"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T09:13:58"}],"detail_url":"/questions/25379","edit_url":"/questions/25379/edit","json_url":"/api/questions/25379","recheck_url":"/api/questions/25379/recheck"},{"id":25361,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1450.pdf","job_source":"人教版.zip","pages":[1,2],"stem":"作圆内接正方形的原理： __________________________________________ 【典例 1】 如图,已知O 的半径为1cm, 求作 O 的内接正八边形. 【典例 2】 若扇形OAB的半径为 6,AOB=120 , 则  AB的长为( ) A.2 B.3 C.4 D.6","options":[],"answer":"中心角是90°，互相垂直的直径把圆4等分","solution":"根据《核心知识点》第2条，作圆内接正方形的原理是：中心角为90°，通过作互相垂直的直径可将圆四等分，从而得到正方形的四个顶点。","stem_html":"<div>作圆内接正方形的原理： __________________________________________<table>\n <thead>\n <tr>\n <th>【典例 1】\n如图,已知O 的半径为1cm, 求作 O\n的内接正八边形.</th>\n <th>【典例 2】\n若扇形OAB的半径为 6,AOB=120 , 则\n\nAB的长为( )\nA.2 B.3 C.4 D.6</th>\n </tr>\n </thead>\n <tbody>\n </tbody>\n</table></div>","answer_html":"中心角是90°，互相垂直的直径把圆4等分","solution_html":"根据《核心知识点》第2条，作圆内接正方形的原理是：中心角为90°，通过作互相垂直的直径可将圆四等分，从而得到正方形的四个顶点。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:04:41"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:04:41"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T09:04:41"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T09:04:54"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:05:30"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:05:30"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:05:30"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T09:05:39"},{"type":"QUALITY_GATE","status":"PASS","score":0.925,"created_at":"2026-09-26T09:05:39"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T09:05:56"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T09:05:56"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T09:05:56"},{"type":"AUTO_FILL_ANSWER","status":"WARN","score":1.0,"created_at":"2026-09-26T09:05:56"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T09:06:17"}],"detail_url":"/questions/25361","edit_url":"/questions/25361/edit","json_url":"/api/questions/25361","recheck_url":"/api/questions/25361/recheck"},{"id":25350,"job_id":3,"qa_status":"QUARANTINED","question_type":"knowledge","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":1.0,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1450.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"作圆内接正方形的原理：中心角是\\(90^{\\circ}\\)，互相垂直的直径把圆4等分，长为\\(\\sqrt{3}r\\)，用半径截弧可得到等分点","options":[],"answer":"","solution":"","stem_html":"<div>作圆内接正方形的原理：中心角是\\(90^{\\circ}\\)，互相垂直的直径把圆4等分，长为\\(\\sqrt{3}r\\)，用半径截弧可得到等分点</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-09-26T09:04:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T09:04:50"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T09:05:27"},{"type":"QUALITY_GATE","status":"FAIL","score":1.0,"created_at":"2026-09-26T09:05:27"}],"detail_url":"/questions/25350","edit_url":"/questions/25350/edit","json_url":"/api/questions/25350","recheck_url":"/api/questions/25350/recheck"},{"id":25342,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"【小试2】 已知：关于x的一元二次方程\\(x^{2}\\)−(2k + 1)x + 2k −1 = 0． （1）求证：无论k为何值, 方程总有两个不相等的实数根; （2）若原方程的两个根是\\(x_{1}\\),\\(x_{2}\\), 满足(\\(x_{1}\\)−2)(\\(x_{2}\\)−2) &lt; 0, 求k的取值范围； （3）当k是整数时，是否存在整数k，使得原方程的根是有理数？若存 在，请求出k的值；若不存在，请说明理由．","options":[],"answer":"(1)见解析；(2)k &gt;\\(1_{2}\\)；(3)不存在整数k，使得原方程的根是有理数，理由见解析．","solution":"(1)\\(\\Delta = (2k + 1)^{2}−4(2k −1) = 4k^{2}−4k + 1 + 4 = (2k −1)^{2}+ 4\\)∵(2k −1)^{2}≥0,所以\\(\\Delta\\)&gt; 0，∴ 无论k为何值时，方程总有两个不相等的实数根. (2)∵\\(x_{1}\\),\\(x_{2}\\)是\\(x^{2}\\)−(2k + 1)x + 2k −1 = 0的根∴\\(x_{1}\\)+\\(x_{2}\\)= 2k + 1,\\(x_{1}x_{2}\\)= 2k-1 ∵(\\(x_{1}\\)−2)(\\(x_{2}\\)−2) &lt; 0,\\(x_{1}x_{2}\\)−2(\\(x_{1}\\)+\\(x_{2}\\)) + 4 &lt; 0代入得2k −1 −2(2k+1) + 4 &lt; 0. 解得k &gt; _{2}∴k的取值范围为k &gt; _{2}.^{1} 1 (3)设方程有有理数根，∴设\\(\\Delta =n^{2}\\), 即(2k + 1)^{2}−4(2k −1) =\\(n^{2}\\), (2k −1)^{2}+4 =\\(n^{2}\\)，\\(n^{2}\\)− (2k −1)^{2}= 4, [n + (2k −1)][n −(2k −1)] = 4, ∵k为整数, n也为整数∴n + (2k −1)和n −(2k −1) 同奇同偶，∴{n + 2k −1 = −2n −(2k −1) = −2或{n + 2k −1 = 2n −(2k −1) = 2 ∴n = 2,2k −1 = 0或n = −2,2k −1 = 0. 即 2k −1 = 0解得k =\\(1_{2}\\)，与k为整数相矛盾，∴不存在整数k，使得原方程的根是有理数．","stem_html":"<div>【小试2】 已知：关于x的一元二次方程\\(x^{2}\\)−(2k + 1)x + 2k −1 = 0．<br>（1）求证：无论k为何值, 方程总有两个不相等的实数根;<br>（2）若原方程的两个根是\\(x_{1}\\),\\(x_{2}\\), 满足(\\(x_{1}\\)−2)(\\(x_{2}\\)−2) &lt; 0, 求k的取值范围；<br>（3）当k是整数时，是否存在整数k，使得原方程的根是有理数？若存 在，请求出k的值；若不存在，请说明理由．</div>","answer_html":"(1)见解析；(2)k &gt;\\(1_{2}\\)；(3)不存在整数k，使得原方程的根是有理数，理由见解析．","solution_html":"(1)\\(\\Delta = (2k + 1)^{2}−4(2k −1) = 4k^{2}−4k + 1 + 4 = (2k −1)^{2}+ 4\\)∵(2k −1)^{2}≥0,所以\\(\\Delta\\)&gt; 0，∴ 无论k为何值时，方程总有两个不相等的实数根. (2)∵\\(x_{1}\\),\\(x_{2}\\)是\\(x^{2}\\)−(2k + 1)x + 2k −1 = 0的根∴\\(x_{1}\\)+\\(x_{2}\\)= 2k + 1,\\(x_{1}x_{2}\\)= 2k-1 ∵(\\(x_{1}\\)−2)(\\(x_{2}\\)−2) &lt; 0,\\(x_{1}x_{2}\\)−2(\\(x_{1}\\)+\\(x_{2}\\)) + 4 &lt; 0代入得2k −1 −2(2k+1) + 4 &lt; 0. 解得k &gt; _{2}∴k的取值范围为k &gt; _{2}.^{1} 1 (3)设方程有有理数根，∴设\\(\\Delta =n^{2}\\), 即(2k + 1)^{2}−4(2k −1) =\\(n^{2}\\), (2k −1)^{2}+4 =\\(n^{2}\\)，\\(n^{2}\\)− (2k −1)^{2}= 4, [n + (2k −1)][n −(2k −1)] = 4, ∵k为整数, n也为整数∴n + (2k −1)和n −(2k −1) 同奇同偶，∴{n + 2k −1 = −2n −(2k −1) = −2或{n + 2k −1 = 2n −(2k −1) = 2 ∴n = 2,2k −1 = 0或n = −2,2k −1 = 0. 即 2k −1 = 0解得k =\\(1_{2}\\)，与k为整数相矛盾，∴不存在整数k，使得原方程的根是有理数．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:59:35"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:59:35"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:59:35"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T09:00:08"}],"detail_url":"/questions/25342","edit_url":"/questions/25342/edit","json_url":"/api/questions/25342","recheck_url":"/api/questions/25342/recheck"},{"id":25346,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"已知关于\\(x^{2}\\)−(m −3)x −m = 0的一元二次方程： （1）试判断原方程根的情况； （2）若抛物线y =\\(x^{2}\\)−(m −3)x −m与x轴交于A(\\(x_{1}\\), 0), B(\\(x_{2}\\), 0)两点，则 A, B两点间的距离是否存在最大或最小值？若存在，求出这个值；若不存在，请说明理由. ( 友情提示：AB = |\\(x_{1}\\)−\\(x_{2}\\)|)","options":[],"answer":"","solution":"","stem_html":"<div>已知关于\\(x^{2}\\)−(m −3)x −m = 0的一元二次方程：<br>（1）试判断原方程根的情况；<br>（2）若抛物线y =\\(x^{2}\\)−(m −3)x −m与x轴交于A(\\(x_{1}\\), 0), B(\\(x_{2}\\), 0)两点，则 A, B两点间的距离是否存在最大或最小值？若存在，求出这个值；若不存在，请说明理由. ( 友情提示：AB = |\\(x_{1}\\)−\\(x_{2}\\)|)</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:55:19"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:55:19"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:55:19"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:55:58"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T08:56:25"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T08:56:25"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:56:25"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:56:44"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T08:56:44"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T09:01:56"},{"type":"CRITIC","status":"FAIL","score":0.8,"created_at":"2026-09-26T09:01:56"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:02:38"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T09:02:38"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T09:02:38"}],"detail_url":"/questions/25346","edit_url":"/questions/25346/edit","json_url":"/api/questions/25346","recheck_url":"/api/questions/25346/recheck"},{"id":25345,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"已知关于x的一元二次方程\\(x^{2}\\)+ 2x + k −2 = 0． （1）若该方程有两个不相等的实数根，求实数k的取值范围； （2）设方程两根为\\(x_{1}\\),\\(x_{2}\\), 是否存在实数k，使\\(x_{1}\\)2 +\\(x_{2} ^{2}\\)= 1? 若存在，求出 实数k；若不存在，请说明理由．","options":[],"answer":"","solution":"","stem_html":"<div>已知关于x的一元二次方程\\(x^{2}\\)+ 2x + k −2 = 0．<br>（1）若该方程有两个不相等的实数根，求实数k的取值范围；<br>（2）设方程两根为\\(x_{1}\\),\\(x_{2}\\), 是否存在实数k，使\\(x_{1}\\)2 +\\(x_{2} ^{2}\\)= 1? 若存在，求出 实数k；若不存在，请说明理由．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:53:56"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:53:56"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:53:56"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:54:25"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:54:57"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T08:54:57"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:54:57"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:55:19"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:55:19"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-09-26T09:00:22"}],"detail_url":"/questions/25345","edit_url":"/questions/25345/edit","json_url":"/api/questions/25345","recheck_url":"/api/questions/25345/recheck"},{"id":25340,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"已知关于\\(x\\)的一元二次方程\\(x^{2} + kx - 4k -16 = 0\\)． (1) 试判断这个方程的根的情况． (2) 是否存在实数\\(k\\),使这个方程的两个根为连续偶数？若存在，求出\\(k\\)的值及方程的根；若不存在，请说明理由．","options":[],"answer":"","solution":"(1)计算判别式：= − 4−1(4k −16) \\(frack^2\\)8)^2 =\\(k^2\\) +16k + 64 = (k +,  任何实数的平方都大于等于即0,(k + 8)^{2}  0, 当k = −8时,= 0,方程有两个相等的实 数根; 当k −8时, 0,方程有两个不相等的 实数根. 综上方程总有两个实数根,. (2)存在实数，使方程两个根为连续偶数k −k (+ 8) 由 知，原方程的根为x =\\(\\frac{k}{2}, \\frac{(1)}{x}\\)即 = 4或x = −−k 4, 由− − =，得 = −,\\(\\frac{k}{k} \\frac{4}{4} \\frac{6}{2} \\frac{k}{k} \\frac{10}{6}\\)由− − =，得 = −， 存在实数 −10,−6，使原方程两个根为 连续偶数．","stem_html":"<div>已知关于\\(x\\)的一元二次方程\\(x^{2} + kx - 4k -16 = 0\\)．\n(1) 试判断这个方程的根的情况．\n(2) 是否存在实数\\(k\\),使这个方程的两个根为连续偶数？若存在，求出\\(k\\)的值及方程的根；若不存在，请说明理由．</div>","answer_html":"","solution_html":"(1)计算判别式：= − 4−1(4k −16)<span class=\"formula-fallback\">\\(frack^2\\)8)^2 =\\(k^2\\)</span>+16k + 64 = (k +,  任何实数的平方都大于等于即0,(k + 8)^{2}  0, 当k = −8时,= 0,方程有两个相等的实 数根; 当k −8时, 0,方程有两个不相等的 实数根. 综上方程总有两个实数根,. (2)存在实数，使方程两个根为连续偶数k −k (+ 8) 由 知，原方程的根为x =\\(\\frac{k}{2}, \\frac{(1)}{x}\\)即 = 4或x = −−k 4, 由− − =，得 = −,\\(\\frac{k}{k} \\frac{4}{4} \\frac{6}{2} \\frac{k}{k} \\frac{10}{6}\\)由− − =，得 = −， 存在实数 −10,−6，使原方程两个根为 连续偶数．","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:53:33"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-09-26T08:53:33"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:53:33"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:54:16"}],"detail_url":"/questions/25340","edit_url":"/questions/25340/edit","json_url":"/api/questions/25340","recheck_url":"/api/questions/25340/recheck"},{"id":25332,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"判断方程\\(x^{2} + (k +1)x + k = 0\\)根的情况____","options":[],"answer":"当k&gt;-1时，方程有两个不相等的实数根；当k=-1时，方程有两个相等的实数根；当k&lt;-1时，方程没有实数根","solution":"计算判别式\\(\\Delta=(k+1)^2-4k=(k-1)^2\\)。由于(k-1)^2≥0恒成立，当k≠1时\\(\\Delta\\)&gt;0，方程有两个不相等的实数根；当k=1时\\(\\Delta=0\\)，方程有两个相等的实数根。","stem_html":"<div>判断方程\\(x^{2} + (k +1)x + k = 0\\)根的情况____</div>","answer_html":"当k&gt;-1时，方程有两个不相等的实数根；当k=-1时，方程有两个相等的实数根；当k&lt;-1时，方程没有实数根","solution_html":"计算判别式\\(\\Delta=(k+1)^2-4k=(k-1)^2\\)。由于(k-1)^2≥0恒成立，当k≠1时\\(\\Delta\\)&gt;0，方程有两个不相等的实数根；当k=1时\\(\\Delta=0\\)，方程有两个相等的实数根。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:46:39"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:46:39"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:46:39"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:47:00"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:47:00"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T08:47:12"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:47:12"},{"type":"COHERENCE","status":"FAIL","score":0.85,"created_at":"2026-09-26T08:50:54"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T08:50:54"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:54:43"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:54:43"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:56:10"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:56:10"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T08:56:10"}],"detail_url":"/questions/25332","edit_url":"/questions/25332/edit","json_url":"/api/questions/25332","recheck_url":"/api/questions/25332/recheck"},{"id":25344,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"已知关于x的一元一次方程(a + c)\\(x^{2}\\)+ 2bx + (a −c) = 0，其中a, b, c分别为△ABC的三边长． （1）如果方程的一个根为−1, 试判断△ABC的形状，并说明理由． （2）如果△ABC是等边三角形, 试求这个一元一次方程的根． （3）如果方程有两个相等的实数根, 试判断△ABC的形状, 并说明理由．","options":[],"answer":"","solution":"","stem_html":"<div>已知关于x的一元一次方程(a + c)\\(x^{2}\\)+ 2bx + (a −c) = 0，其中a, b, c分别为△ABC的三边长．<br>（1）如果方程的一个根为−1, 试判断△ABC的形状，并说明理由．<br>（2）如果△ABC是等边三角形, 试求这个一元一次方程的根．<br>（3）如果方程有两个相等的实数根, 试判断△ABC的形状, 并说明理由．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:51:58"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:51:58"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:51:58"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:52:30"}],"detail_url":"/questions/25344","edit_url":"/questions/25344/edit","json_url":"/api/questions/25344","recheck_url":"/api/questions/25344/recheck"},{"id":25339,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.725,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"已知关于的一元二次方程x(a +) + 2bx +\\(\\frac{cx^{2}}{ABC} (−) = 0\\)a,b,c分别为 三边的长．\\(\\frac{a}{(1)}\\frac{c}{如果} \\frac{其中}{1}\\)x = − 是方程的根,试判断 ABC的形 状,并说明理由; （1）如果方程有两个相等的实数根,试判断  ABC的形状,并说明理由.","options":[],"answer":"","solution":"(把 = −1代入方程： frac1)a fracxc (+ − + 2 (−1) + (a − c) = 0, frac)(1)^2b fracbc + c − 2 + a − = 0,\\(\\frac{a}{2}\\)a − 2b = 0, a = b,  a = b,  ABC是等腰三角形. (2)一元二次方程有两个相等实根说明,= 0, 则= b − a + c)(a − c) = 0, frac(2)^\\(2a^2\\) frac4(\\(c^24b^2\\) − 4(−) = 0, − + = 0, \\(fracb^2a^2fraca^2b^2fracc^2c^2\\) = + 根据勾股定理逆定理，  ABC是直角三角形且, = 90. A","stem_html":"<div>已知关于的一元二次方程x(a +) + 2bx +\\(\\frac{cx^{2}}{ABC} (−) = 0\\)a,b,c分别为 三边的长．\\(\\frac{a}{(1)}\\frac{c}{如果} \\frac{其中}{1}\\)x = − 是方程的根,试判断 ABC的形 状,并说明理由;<br>（1）如果方程有两个相等的实数根,试判断  ABC的形状,并说明理由.</div>","answer_html":"","solution_html":"(把 = −1代入方程：<span class=\"formula-fallback\">frac1)a fracxc (+ − + 2 (−1) + (a − c) = 0, frac)(1)^2b fracbc +</span>c − 2 + a − = 0,\\(\\frac{a}{2}\\)a − 2b = 0, a = b,  a = b,  ABC是等腰三角形. (2)一元二次方程有两个相等实根说明,= 0, 则= b − a + c)(a − c) = 0,<span class=\"formula-fallback\">frac(2)^\\(2a^2\\) frac4(\\(c^24b^2\\) − 4(−) = 0, − + = 0, \\(fracb^2a^2fraca^2b^2fracc^2c^2\\) = +</span> 根据勾股定理逆定理，  ABC是直角三角形且, = 90. A","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:50:28"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-09-26T08:50:28"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:50:28"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T08:51:18"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:51:20"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:51:20"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:51:20"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T08:52:38"},{"type":"QUALITY_GATE","status":"FAIL","score":0.725,"created_at":"2026-09-26T08:52:38"}],"detail_url":"/questions/25339","edit_url":"/questions/25339/edit","json_url":"/api/questions/25339","recheck_url":"/api/questions/25339/recheck"},{"id":25328,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"判断方程\\(x^{2}\\)+ (k − 2)x − 2k = 0 根的情况___","options":[],"answer":"有两个不相等的实数根","solution":"计算判别式\\(\\Delta = (k-2)^2 - 4\\times 1\\times (-2k) =k^{2}\\)- 4k + 4 + 8k =\\(k^{2}\\)+ 4k + 4 = (k+2)^2。由于 (k+2)^2 ≥ 0 恒成立，且当 k = -2 时\\(\\Delta = 0\\)，当 k ≠ -2 时\\(\\Delta\\)&gt; 0。但题目未指定 k 值，故需分情况：若 k ≠ -2，则\\(\\Delta\\)&gt; 0，方程有两个不相等实数根；若 k = -2，则\\(\\Delta = 0\\)，方程有两个相等实数根。然而，观察原方程可因式分解为 (x+2)(x+(k-2))=0，根为 x=-2 和 x=2-k，两者仅在 k=0 时相等。但根据判别式分析，更严谨的结论是：对于任意实数 k，\\(\\Delta=(k+2)^2≥0\\)，因此方程总有实数根，且当 k≠-2 时两根不等，k=-2 时两根相等。","stem_html":"<div>判断方程\\(x^{2}\\)+ (k − 2)x − 2k = 0 根的情况___</div>","answer_html":"有两个不相等的实数根","solution_html":"计算判别式\\(\\Delta = (k-2)^2 - 4\\times 1\\times (-2k) =k^{2}\\)- 4k + 4 + 8k =\\(k^{2}\\)+ 4k + 4 = (k+2)^2。由于 (k+2)^2 ≥ 0 恒成立，且当 k = -2 时\\(\\Delta = 0\\)，当 k ≠ -2 时\\(\\Delta\\)&gt; 0。但题目未指定 k 值，故需分情况：若 k ≠ -2，则\\(\\Delta\\)&gt; 0，方程有两个不相等实数根；若 k = -2，则\\(\\Delta = 0\\)，方程有两个相等实数根。然而，观察原方程可因式分解为 (x+2)(x+(k-2))=0，根为 x=-2 和 x=2-k，两者仅在 k=0 时相等。但根据判别式分析，更严谨的结论是：对于任意实数 k，\\(\\Delta=(k+2)^2≥0\\)，因此方程总有实数根，且当 k≠-2 时两根不等，k=-2 时两根相等。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:44:47"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:44:47"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:44:47"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:45:12"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:45:44"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:45:44"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:45:44"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:46:44"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T08:46:44"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-09-26T08:51:36"}],"detail_url":"/questions/25328","edit_url":"/questions/25328/edit","json_url":"/api/questions/25328","recheck_url":"/api/questions/25328/recheck"},{"id":25335,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"判断方程\\(x^{2} - kx + (k - 1) = 0\\)根的情况___","options":[],"answer":"当k&lt;2时，方程有两个不相等的实数根；当k=2时，方程有两个相等的实数根；当k&gt;2时，方程没有实数根","solution":"计算判别式\\(\\Delta = (-k)^2 - 4\\times 1\\times (k-1) =k^{2}\\)- 4k + 4 = (k-2)^2。由于(k-2)^2 ≥ 0恒成立，当k≠2时\\(\\Delta\\)&gt;0，方程有两个不相等的实数根；当k=2时\\(\\Delta=0\\)，方程有两个相等的实数根。","stem_html":"<div>判断方程\\(x^{2} - kx + (k - 1) = 0\\)根的情况___</div>","answer_html":"当k&lt;2时，方程有两个不相等的实数根；当k=2时，方程有两个相等的实数根；当k&gt;2时，方程没有实数根","solution_html":"计算判别式\\(\\Delta = (-k)^2 - 4\\times 1\\times (k-1) =k^{2}\\)- 4k + 4 = (k-2)^2。由于(k-2)^2 ≥ 0恒成立，当k≠2时\\(\\Delta\\)&gt;0，方程有两个不相等的实数根；当k=2时\\(\\Delta=0\\)，方程有两个相等的实数根。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:46:44"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:46:44"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:46:44"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:46:58"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:47:46"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:47:46"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:47:46"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:47:53"},{"type":"QUALITY_GATE","status":"PASS","score":0.925,"created_at":"2026-09-26T08:47:53"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:48:18"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T08:48:18"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:48:43"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:48:43"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:48:43"}],"detail_url":"/questions/25335","edit_url":"/questions/25335/edit","json_url":"/api/questions/25335","recheck_url":"/api/questions/25335/recheck"},{"id":25329,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"判断方程\\(x^{2} + kx - 2k - 4 = 0\\)根的情况____","options":[],"answer":"当k&gt;2或k&lt;-2时，方程有两个不相等的实数根；当k=2或k=-2时，方程有两个相等的实数根；当-2&lt;k&lt;2时，方程没有实数根","solution":"计算判别式\\(\\Delta =k^{2}\\)- 4(1)(-2k-4) =\\(k^{2}\\)+ 8k + 16 = (k+4)^2。由于(k+4)^2 ≥ 0恒成立，且仅当k=-4时\\(\\Delta=0\\)，因此：当k≠-4时\\(\\Delta\\)&gt;0，方程有两个不相等的实数根；当k=-4时\\(\\Delta=0\\)，方程有两个相等的实数根。","stem_html":"<div>判断方程\\(x^{2} + kx - 2k - 4 = 0\\)根的情况____</div>","answer_html":"当k&gt;2或k&lt;-2时，方程有两个不相等的实数根；当k=2或k=-2时，方程有两个相等的实数根；当-2&lt;k&lt;2时，方程没有实数根","solution_html":"计算判别式\\(\\Delta =k^{2}\\)- 4(1)(-2k-4) =\\(k^{2}\\)+ 8k + 16 = (k+4)^2。由于(k+4)^2 ≥ 0恒成立，且仅当k=-4时\\(\\Delta=0\\)，因此：当k≠-4时\\(\\Delta\\)&gt;0，方程有两个不相等的实数根；当k=-4时\\(\\Delta=0\\)，方程有两个相等的实数根。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:44:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:44:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:44:17"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:44:25"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:45:10"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:45:10"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:45:10"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T08:45:51"},{"type":"QUALITY_GATE","status":"PASS","score":0.95,"created_at":"2026-09-26T08:45:51"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:46:12"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:46:12"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T08:47:27"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:47:27"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T08:47:27"}],"detail_url":"/questions/25329","edit_url":"/questions/25329/edit","json_url":"/api/questions/25329","recheck_url":"/api/questions/25329/recheck"},{"id":25327,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"判断方程\\(x^{2} - kx + (k - 1) = 0\\)根的情况____","options":[],"answer":"有两个不相等的实数根","solution":"计算判别式\\(\\Delta =b^{2}\\)- 4ac = (-k)^2 -\\(4\\times 1\\times (k-1) =k^{2}\\)- 4k + 4 = (k-2)^2。由于 (k-2)^2 ≥ 0 恒成立，且当 k≠2 时\\(\\Delta\\)&gt;0，当 k=2 时\\(\\Delta=0\\)。但题目未指定k值，故需讨论：当k≠2时，方程有两个不相等的实数根；当k=2时，方程有两个相等的实数根。","stem_html":"<div>判断方程\\(x^{2} - kx + (k - 1) = 0\\)根的情况____</div>","answer_html":"有两个不相等的实数根","solution_html":"计算判别式\\(\\Delta =b^{2}\\)- 4ac = (-k)^2 -\\(4\\times 1\\times (k-1) =k^{2}\\)- 4k + 4 = (k-2)^2。由于 (k-2)^2 ≥ 0 恒成立，且当 k≠2 时\\(\\Delta\\)&gt;0，当 k=2 时\\(\\Delta=0\\)。但题目未指定k值，故需讨论：当k≠2时，方程有两个不相等的实数根；当k=2时，方程有两个相等的实数根。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:43:53"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:43:53"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:43:53"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:44:05"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:44:56"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:44:56"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:44:56"},{"type":"COHERENCE","status":"PASS","score":0.8,"created_at":"2026-09-26T08:45:09"},{"type":"QUALITY_GATE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:45:09"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T08:45:51"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:45:51"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:46:24"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:46:24"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:46:24"}],"detail_url":"/questions/25327","edit_url":"/questions/25327/edit","json_url":"/api/questions/25327","recheck_url":"/api/questions/25327/recheck"},{"id":25325,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案145.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"判断方程\\(x^{2} - (k + 3)x + 3k = 0\\)根的情况___","options":[],"answer":"当k&gt;3时，方程有两个不相等的实数根；当k=3时，方程有两个相等的实数根；当k&lt;3时，方程没有实数根","solution":"计算判别式\\(\\Delta = [-(k+3)]^2 - 4\\times 1\\times 3k = (k+3)^2 - 12k =k^{2}\\)+ 6k + 9 - 12k =\\(k^{2}\\)- 6k + 9 = (k-3)^2。由于(k-3)^2 ≥ 0恒成立，当k≠3时\\(\\Delta\\)&gt;0，方程有两个不相等实数根；当k=3时\\(\\Delta=0\\)，方程有两个相等实数根。但题目未指定k的取值范围，因此需分情况讨论。","stem_html":"<div>判断方程\\(x^{2} - (k + 3)x + 3k = 0\\)根的情况___</div>","answer_html":"当k&gt;3时，方程有两个不相等的实数根；当k=3时，方程有两个相等的实数根；当k&lt;3时，方程没有实数根","solution_html":"计算判别式\\(\\Delta = [-(k+3)]^2 - 4\\times 1\\times 3k = (k+3)^2 - 12k =k^{2}\\)+ 6k + 9 - 12k =\\(k^{2}\\)- 6k + 9 = (k-3)^2。由于(k-3)^2 ≥ 0恒成立，当k≠3时\\(\\Delta\\)&gt;0，方程有两个不相等实数根；当k=3时\\(\\Delta=0\\)，方程有两个相等实数根。但题目未指定k的取值范围，因此需分情况讨论。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:43:18"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:43:18"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:43:18"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:43:40"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:44:22"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:44:22"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:44:22"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:44:32"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T08:44:32"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:45:44"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:45:44"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:46:05"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:46:05"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:46:05"}],"detail_url":"/questions/25325","edit_url":"/questions/25325/edit","json_url":"/api/questions/25325","recheck_url":"/api/questions/25325/recheck"},{"id":25306,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1445.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图，等边ABC内接于 O, BD为 O 内接正十二边形的一边，CD=\\(5 \\sqrt{2}\\)则 图中阴影部分的面积等于 ______.","options":[],"answer":"\\(\\frac{25}{4}− \\frac{25}{2}．\\)","solution":"连接OB,OC,OD,等边 ABC内接于 O, BD为内接正十二边形的一边， BOC =\\(\\frac{1}{3}\\) =120,BOD =\\(\\frac{1}{12}\\)360 = 30，\\(\\frac{360}{BOC}\\)COD =  −BOD = 90,  = OD, = 45,\\(OC^{2}\\)+\\(OD^{2}\\)=\\(CD^{2}\\).\\(\\frac{OC}{2} \\frac{OCD}{OC}\\)即\\(OC^{2}\\)= 50, = 5. 9025 S阴影 = S扇形 − S OCD = −\\(\\frac{1}{2}\\)55 OCD  360 =\\(\\frac{25}{4}− \\frac{25}{2}．\\)故答案为\\(\\frac{25}{4}− \\frac{25}{2}．\\)","stem_html":"<div>如图，等边ABC内接于 O, BD为 O 内接正十二边形的一边，CD=\\(5 \\sqrt{2}\\)则 图中阴影部分的面积等于 ______.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/2f898197-b79c-4400-ac2d-3cc0bcd0ee28/715dbd20597d.png\" style=\"width:126.7px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"\\(\\frac{25}{4}− \\frac{25}{2}．\\)","solution_html":"连接OB,OC,OD,等边 ABC内接于 O, BD为内接正十二边形的一边， BOC =\\(\\frac{1}{3}\\) =120,BOD =\\(\\frac{1}{12}\\)360 = 30，\\(\\frac{360}{BOC}\\)COD =  −BOD = 90,  = OD, = 45,\\(OC^{2}\\)+\\(OD^{2}\\)=\\(CD^{2}\\).\\(\\frac{OC}{2} \\frac{OCD}{OC}\\)即\\(OC^{2}\\)= 50, = 5. 9025 S阴影 = S扇形 − S OCD = −\\(\\frac{1}{2}\\)55 OCD  360 =\\(\\frac{25}{4}− \\frac{25}{2}．\\)故答案为\\(\\frac{25}{4}− \\frac{25}{2}．\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:39:01"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:39:01"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:39:01"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:39:36"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T08:41:36"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:41:36"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:41:36"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:42:01"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T08:42:01"}],"detail_url":"/questions/25306","edit_url":"/questions/25306/edit","json_url":"/api/questions/25306","recheck_url":"/api/questions/25306/recheck"},{"id":25308,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1445.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"[小试2] 如图，等边△ABC内接于⊙O,BD为⊙O内接正十二边形的一边，CD=10√2，则图中阴影部分的面积等于________.","options":[],"answer":"","solution":"","stem_html":"<div>[小试2]\n如图，等边△ABC内接于⊙O,BD为⊙O内接正十二边形的一边，CD=10√2，则图中阴影部分的面积等于________.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/3ad5dee2-cbd8-4500-9e20-a2d87999f787/45caee1a4655.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:31:59"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:31:59"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:31:59"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:32:26"},{"type":"SOLVER","status":"PASS","score":0.85,"created_at":"2026-09-26T08:32:39"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T08:32:39"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:32:39"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:33:17"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:33:17"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T08:36:10"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T08:36:10"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:37:45"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:37:45"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.85,"created_at":"2026-09-26T08:37:45"}],"detail_url":"/questions/25308","edit_url":"/questions/25308/edit","json_url":"/api/questions/25308","recheck_url":"/api/questions/25308/recheck"},{"id":25312,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1445.pdf","job_source":"人教版.zip","pages":[4,5],"stem":"如图, 点A, B, C在⊙O上, 若BC, AB, AC分别是⊙O内接正三角形. 正方形,正n边形的一边，则n = ( ) A. \\(9 \\frac{(B)10}{(C)12}\\) D. 15","options":[{"label":"A","text":"9 \\frac{(B)10}{(C)12}"},{"label":"D","text":"15"}],"answer":"","solution":"","stem_html":"<div>如图, 点A, B, C在⊙O上, 若BC, AB, AC分别是⊙O内接正三角形. 正方形,正n边形的一边，则n = ( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/197b06f9-81bb-4059-a756-4eef3f421270/06a560d758c0.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(9 \\frac{(B)10}{(C)12}\\)<br>D. 15</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:33:35"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:33:35"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:33:35"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:34:32"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T08:36:26"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:36:26"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:36:26"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:36:57"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T08:36:57"}],"detail_url":"/questions/25312","edit_url":"/questions/25312/edit","json_url":"/api/questions/25312","recheck_url":"/api/questions/25312/recheck"},{"id":25280,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.913,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1440.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如 图，在正六边形ABCDEF中，M, N分别为边CD, BC的中点，AN与B M相交于点P，则∠NPM的度数是( ) A. 50∘ B. 60∘ C. 70∘ D. 120∘","options":[{"label":"A","text":"50∘"},{"label":"B","text":"60∘"},{"label":"C","text":"70∘"},{"label":"D","text":"120∘"}],"answer":"","solution":"","stem_html":"<div>如 图，在正六边形ABCDEF中，M, N分别为边CD, BC的中点，AN与B M相交于点P，则∠NPM的度数是( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/d0e4347e-593e-4e08-9300-60aaf4dca655/45226fc27738.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 50∘<br>B. 60∘<br>C. 70∘<br>D. 120∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:18:55"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:18:55"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:18:55"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:19:40"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:20:35"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:20:35"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:20:35"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T08:20:45"},{"type":"QUALITY_GATE","status":"FAIL","score":0.913,"created_at":"2026-09-26T08:20:45"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:25:01"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:25:01"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:25:36"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:25:36"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:25:36"}],"detail_url":"/questions/25280","edit_url":"/questions/25280/edit","json_url":"/api/questions/25280","recheck_url":"/api/questions/25280/recheck"},{"id":25281,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1440.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，在正六边形ABCDEF中，M, N分别是边BC, CD上的点，且CM=DN, AM与BN交于点Q． （1）求证：△ABM ≅△BCN； （2）求∠AQB的度数．","options":[],"answer":"","solution":"","stem_html":"<div>如图，在正六边形ABCDEF中，M, N分别是边BC, CD上的点，且CM=DN, AM与BN交于点Q．<br>（1）求证：△ABM ≅△BCN；<br>（2）求∠AQB的度数．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:20:07"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:20:07"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:20:07"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T08:20:27"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:21:09"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:21:09"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:21:09"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:21:18"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T08:21:18"}],"detail_url":"/questions/25281","edit_url":"/questions/25281/edit","json_url":"/api/questions/25281","recheck_url":"/api/questions/25281/recheck"},{"id":25275,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1440.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"点\\(F\\)是正五边形 $ABCDE 边\\(DE\\)的中点，连接\\(BF\\)并延长，与\\(CD\\)延长线交于点\\(G\\). 则\\(angle BGC\\)的度数为 ____.","options":[],"answer":"","solution":"","stem_html":"<div>点\\(F\\)是正五边形 $ABCDE<span class=\"formula-fallback\"> 边\\(DE\\)的中点，连接\\(BF\\)并延长，与\\(CD\\)延长线交于点\\(G\\). 则\\(angle BGC\\)的度数为 ____.</span><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/5cb11d49-88c7-40e1-ba77-bd4930e31da5/fef1646ad27f.png\" style=\"width:192.0px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:17:48"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:17:48"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:17:48"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:17:55"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:19:42"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:19:42"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:19:42"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:19:52"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T08:19:52"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T08:23:05"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T08:23:05"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:23:55"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:23:55"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:23:55"}],"detail_url":"/questions/25275","edit_url":"/questions/25275/edit","json_url":"/api/questions/25275","recheck_url":"/api/questions/25275/recheck"},{"id":25277,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1440.pdf","job_source":"人教版.zip","pages":[3,4],"stem":"【小试2】 如图，正五边形 ABCDE 中，F 为 CD 边中点，连接 AF、CA，则∠CAF的度数 ( ) (A)18∘ (B)30∘ (C)36∘ (D)54∘ Col1 A. 18∘ B. 30∘ C. 36∘ D. 54∘","options":[{"label":"A","text":"18∘"},{"label":"B","text":"30∘"},{"label":"C","text":"36∘"},{"label":"D","text":"54∘"}],"answer":"A","solution":"如图，连接AD，∵五边形ABCDE是正五边形，∴AB = BC = AE = ED，∠ABC = ∠AED = ∠BAE = 108°，∴△ABC ≅ △AED，∴AC = AD，∠CAB = ∠DAE = 36°，∴∠CAD = 36°，∵CF = DF，∴∠CAF = ∠DAF = 18°，故选A.","stem_html":"<div>【小试2】 如图，正五边形 ABCDE 中，F 为 CD 边中点，连接 AF、CA，则∠CAF的度数 ( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/a749c637-2624-4203-9b2e-ae2fd60a7a80/0c1bd250f798.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/a749c637-2624-4203-9b2e-ae2fd60a7a80/f910be8ff78d.png\" style=\"width:54.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><table>\n <thead>\n <tr>\n <th>(A)18∘\n(B)30∘\n(C)36∘\n(D)54∘</th>\n <th>Col1</th>\n </tr>\n </thead>\n <tbody>\n </tbody>\n</table><br>A. 18∘<br>B. 30∘<br>C. 36∘<br>D. 54∘</div>","answer_html":"A","solution_html":"如图，连接AD，∵五边形ABCDE是正五边形，∴AB = BC = AE = ED，∠ABC = ∠AED = ∠BAE = 108°，∴△ABC ≅ △AED，∴AC = AD，∠CAB = ∠DAE = 36°，∴∠CAD = 36°，∵CF = DF，∴∠CAF = ∠DAF = 18°，故选A.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:19:27"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:19:27"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:19:27"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T08:19:54"}],"detail_url":"/questions/25277","edit_url":"/questions/25277/edit","json_url":"/api/questions/25277","recheck_url":"/api/questions/25277/recheck"},{"id":25274,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1440.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"某同学在学习割圆术的过程中作了一\"\", 个圆内接正十二边形若. O的半径为2, 则这个圆内接正十二边形的面积为( ) .3 .12 .4 .12 A B C D","options":[],"answer":"18.","solution":"【讲解】 正十二边形的中心角为\\(\\frac{360}{12}=\\) 30. 每个小三角形的面积为\\(\\frac{1}{2}\\)22sin30=1, 正十二边形的面积 =12=1 故选 12. B 连接BD, BE.  五边形ABCDE是正五边形，  = BC = = AE, = .\\(\\frac{AB}{ABE} \\frac{CD}{CBDSAS}\\)A C   (), BE = BD.  点是DE的中点， F BG是DE的垂直平分线，DFG = 90 . fracABCDE2)180  在正五边形 中， (5 −    = =108,\\(\\frac{CDE}{FDG} 5\\) = 180 − = 72,\\(\\frac{CDE}{DFG}\\) = 180  − −FDG G = 180− 90 − 72 =18 . 故答案为：18.","stem_html":"<div>某同学在学习割圆术的过程中作了一\"\", 个圆内接正十二边形若. O的半径为2, 则这个圆内接正十二边形的面积为( ) .3 .12 .4 .12 A B C D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/31de3d3b-217e-4b0a-9a30-856785c297ec/288304939129.png\" style=\"width:148.8px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"18.","solution_html":"【讲解】 正十二边形的中心角为\\(\\frac{360}{12}=\\) 30. 每个小三角形的面积为\\(\\frac{1}{2}\\)22sin30=1, 正十二边形的面积 =12=1 故选 12. B 连接BD, BE.  五边形ABCDE是正五边形，  = BC = = AE, = .\\(\\frac{AB}{ABE} \\frac{CD}{CBDSAS}\\)A C   (), BE = BD.  点是DE的中点， F BG是DE的垂直平分线，DFG = 90 .<span class=\"formula-fallback\">fracABCDE2)180</span> 在正五边形 中， (5 −    = =108,\\(\\frac{CDE}{FDG} 5\\) = 180 − = 72,\\(\\frac{CDE}{DFG}\\) = 180  − −FDG G = 180− 90 − 72 =18 . 故答案为：18.","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:20:48"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-09-26T08:20:48"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:20:48"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:21:42"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:21:55"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:21:55"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:21:55"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T08:22:50"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T08:22:50"}],"detail_url":"/questions/25274","edit_url":"/questions/25274/edit","json_url":"/api/questions/25274","recheck_url":"/api/questions/25274/recheck"},{"id":25278,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1440.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"我国魏晋时期数学家刘徽在《九章算术注》中提到著名的\"割圆术\"，即 利用圆的内接正多边形逼近圆的方法来近似估算，指出\"割之弥细，所失弥少. 割之又割，以至于不可割，则与圆周合体，而无所失 矣\"．\"割圆术\"孕育了微积分思想，他用这种思想得到了圆周率\\(\\pi\\)的近似值为3.1416, 如图, 若⊙ O的半径为1．(在求圆内接正多边形面积时，通过分割成三角形，利用特殊角解决) （1）求圆内接正六边形面积． （2）圆内接正八边形的面积为______. （3）运用＂割圆术＂，用圆内接正十二边形近似估计⊙O的面积，可得圆内接正十二边形面积是 ______，可得\\(\\pi\\)的估计值为______．","options":[],"answer":"","solution":"","stem_html":"<div>我国魏晋时期数学家刘徽在《九章算术注》中提到著名的\"割圆术\"，即 利用圆的内接正多边形逼近圆的方法来近似估算，指出\"割之弥细，所失弥少. 割之又割，以至于不可割，则与圆周合体，而无所失 矣\"．\"割圆术\"孕育了微积分思想，他用这种思想得到了圆周率\\(\\pi\\)的近似值为3.1416, 如图, 若⊙ O的半径为1．(在求圆内接正多边形面积时，通过分割成三角形，利用特殊角解决)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/0144be21-8720-4d24-870e-d883e4a2bbbc/bd129db18fdd.png\" style=\"width:188.7px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）求圆内接正六边形面积．<br>（2）圆内接正八边形的面积为______.<br>（3）运用＂割圆术＂，用圆内接正十二边形近似估计⊙O的面积，可得圆内接正十二边形面积是 ______，可得\\(\\pi\\)的估计值为______．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:18:13"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:18:13"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:18:13"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T08:18:48"}],"detail_url":"/questions/25278","edit_url":"/questions/25278/edit","json_url":"/api/questions/25278","recheck_url":"/api/questions/25278/recheck"},{"id":25279,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.912,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1440.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，已知正八边形$ABCDEFGH 是半径为\\(4sqrt2\\)的\\(odot O\\)内接八边形，求阴影部分图形的面积．","options":[],"answer":"","solution":"","stem_html":"<div>如图，已知正八边形$ABCDEFGH<span class=\"formula-fallback\">是半径为\\(4sqrt2\\)的\\(odot O\\)内接八边形，求阴影部分图形的面积．</span></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-09-26T08:19:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:19:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:19:11"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T08:19:21"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T08:19:58"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:19:58"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:19:58"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:20:11"},{"type":"QUALITY_GATE","status":"FAIL","score":0.912,"created_at":"2026-09-26T08:20:11"}],"detail_url":"/questions/25279","edit_url":"/questions/25279/edit","json_url":"/api/questions/25279","recheck_url":"/api/questions/25279/recheck"},{"id":25242,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1435.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图所示,Rt△ ABC的内切圆分别与AB、 BC相切于D点、 E点，若BD= 1cm, AD = 4cm, 则CE的长为____.","options":[],"answer":"\\(\\frac{5}{3} \\, \\mathrm{cm}\\)","solution":"设CE =xcm,∵ Rt△ ABC的内切圆分别与AB、 BC相切于D点、 E点所以 BD=BE = 1cm,BC = (x+ 1)cm,CF =CE =xcm,AF =AD= 4cm,则 AC= AD + CE= 4 + x(cm), 在Rt △ABC中,\\(AB^{2}\\)+\\(BC^{2}\\)=\\(AC^{2}\\), ∴AC= AD+CE = 4 +x(cm),解得x=\\(\\frac{5}{3}\\)即CE的长度为\\(\\frac{5}{3}\\)cm.故答案为\\(\\frac{5}{3}\\)cm.","stem_html":"<div>如图所示,Rt△ ABC的内切圆分别与AB、 BC相切于D点、 E点，若BD= 1cm, AD = 4cm, 则CE的长为____.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/94de1a7b-1164-4adb-93ba-f47db1879fc4/f5dc9217d13c.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"\\(\\frac{5}{3} \\, \\mathrm{cm}\\)","solution_html":"设CE =xcm,∵ Rt△ ABC的内切圆分别与AB、 BC相切于D点、 E点所以 BD=BE = 1cm,BC = (x+ 1)cm,CF =CE =xcm,AF =AD= 4cm,则 AC= AD + CE= 4 + x(cm),  在Rt △ABC中,\\(AB^{2}\\)+\\(BC^{2}\\)=\\(AC^{2}\\), ∴AC= AD+CE = 4 +x(cm),解得x=\\(\\frac{5}{3}\\)即CE的长度为\\(\\frac{5}{3}\\)cm.故答案为\\(\\frac{5}{3}\\)cm.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:07:08"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:07:08"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:07:08"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:08:08"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:08:21"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:08:21"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:08:21"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:09:51"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T08:09:51"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:11:21"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:11:21"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T08:12:03"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:12:03"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T08:12:03"}],"detail_url":"/questions/25242","edit_url":"/questions/25242/edit","json_url":"/api/questions/25242","recheck_url":"/api/questions/25242/recheck"},{"id":25246,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.967,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1435.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，\\(A\\)、\\(B\\)、\\(C\\)、\\(D\\)为一个正多边形的相邻四个顶点，\\(O\\)是正多边形的中心，若\\(\\angle ADB = 15^\\circ\\)，则这个正多边形的边数为____．","options":[],"answer":"12","solution":"如图，设正多边形的外接圆为\\(\\odot O\\)，连接$OA,OB ，\\(because angle ADB= 15^circ\\)，所以\\(angle AOB= 2angle ADB= 30^circ\\)，\\(therefore\\)这个正多边形为\\(360^circdiv 30^circ= 12\\)，故答案为：12．","stem_html":"<div>如图，\\(A\\)、\\(B\\)、\\(C\\)、\\(D\\)为一个正多边形的相邻四个顶点，\\(O\\)是正多边形的中心，若\\(\\angle ADB = 15^\\circ\\)，则这个正多边形的边数为____．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/41d9f74d-9a58-4e59-979d-f8a3ea885016/95d1af5ef6ce.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"12","solution_html":"如图，设正多边形的外接圆为\\(\\odot O\\)，连接$OA,OB<span class=\"formula-fallback\">，\\(because angle ADB= 15^circ\\)，所以\\(angle AOB= 2angle ADB= 30^circ\\)，\\(therefore\\)这个正多边形为\\(360^circdiv 30^circ= 12\\)，故答案为：12．</span>","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:08:46"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:08:46"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:08:46"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T08:09:04"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:09:04"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T08:09:29"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:09:29"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T08:10:17"},{"type":"QUALITY_GATE","status":"FAIL","score":0.967,"created_at":"2026-09-26T08:10:17"}],"detail_url":"/questions/25246","edit_url":"/questions/25246/edit","json_url":"/api/questions/25246","recheck_url":"/api/questions/25246/recheck"},{"id":25245,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":1,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.975,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1435.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图所示，正方形ABCD是 ⊙ O的内接四边形，若 ⊙ O的半径为8，则正方形ABCD的边长为 ____．","options":[],"answer":"8√2","solution":"因为正方形\\(ABCD\\)是\\odot O的内接四边形，\\(\\therefore \\angle BOC = 360^{\\circ} \\times \\frac{1}{4} = 90^{\\circ}\\)，因为\\(\\odot O\\)的半径为8，\\(\\therefore OB = OC = 8\\)，\\(\\therefore BC = \\sqrt{8^{2} + 8^{2}} = 8\\sqrt{2}\\)，\\(\\therefore\\)正方形\\)ABCD\\)的边长为 8sqrt2 。故答案为：\\(8\\sqrt{2}．","stem_html":"<div>如图所示，正方形ABCD是 ⊙ O的内接四边形，若 ⊙ O的半径为8，则正方形ABCD的边长为 ____．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/03b1c5ad-8ca4-4e92-9106-701ded64b3d9/eef8c0edfb9d.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"8√2","solution_html":"因为正方形\\(ABCD\\)是\\odot O的内接四边形，\\(\\therefore \\angle BOC = 360^{\\circ} \\times \\frac{1}{4} = 90^{\\circ}\\)，因为\\(\\odot O\\)的半径为8，\\(\\therefore OB = OC = 8\\)，\\(\\therefore BC = \\sqrt{8^{2} + 8^{2}} = 8\\sqrt{2}\\)，\\(\\therefore\\)正方形\\)ABCD\\)的边长为<span class=\"formula-fallback\">8sqrt2</span>。故答案为：\\(8\\sqrt{2}．","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:07:16"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:07:16"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:07:16"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T08:07:33"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:08:15"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:08:15"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:08:15"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T08:08:31"},{"type":"QUALITY_GATE","status":"PASS","score":0.975,"created_at":"2026-09-26T08:08:31"}],"detail_url":"/questions/25245","edit_url":"/questions/25245/edit","json_url":"/api/questions/25245","recheck_url":"/api/questions/25245/recheck"},{"id":25236,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1435.pdf","job_source":"人教版.zip","pages":[1,2],"stem":"如图，点A,B,C,D为一个正多边形的部分顶点，点O为正多边形的中 心，若∠AOD = 120°，则这个正多边形的边数为( ). A. \\(\\frac{6}{9}\\) B. C. 10 D. 12","options":[{"label":"A","text":"\\frac{6}{9}"},{"label":"B","text":""},{"label":"C","text":"10"},{"label":"D","text":"12"}],"answer":"12","solution":"连接OB。因为点A、B、C、D是正多边形的连续顶点，O是中心，所以∠AOB、∠BOC、∠COD都是相等的中心角。已知∠AOD = 120°，且∠AOD = ∠AOB + ∠BOC + ∠COD =\\(3 \\times\\)∠AOB，因此∠AOB = 120° ÷ 3 = 40°。正多边形的边数 n = 360° ÷ 中心角 = 360° ÷ 40° = 12。","stem_html":"<div>如图，点A,B,C,D为一个正多边形的部分顶点，点O为正多边形的中 心，若∠AOD = 120°，则这个正多边形的边数为(  ).<br>A. \\(\\frac{6}{9}\\)<br>B. <br>C. 10<br>D. 12</div>","answer_html":"12","solution_html":"连接OB。因为点A、B、C、D是正多边形的连续顶点，O是中心，所以∠AOB、∠BOC、∠COD都是相等的中心角。已知∠AOD = 120°，且∠AOD = ∠AOB + ∠BOC + ∠COD =\\(3 \\times\\)∠AOB，因此∠AOB = 120° ÷ 3 = 40°。正多边形的边数 n = 360° ÷ 中心角 = 360° ÷ 40° = 12。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:02:16"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:02:16"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:02:16"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T08:02:32"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:02:32"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:02:54"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:02:54"},{"type":"COHERENCE","status":"FAIL","score":0.85,"created_at":"2026-09-26T08:04:18"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T08:04:18"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T08:05:35"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T08:05:35"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T08:06:55"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T08:06:55"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T08:06:55"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-09-26T08:06:55"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:07:38"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/25236","edit_url":"/questions/25236/edit","json_url":"/api/questions/25236","recheck_url":"/api/questions/25236/recheck"},{"id":25243,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.967,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1435.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图所示，PA,PB是 ⊙ O的切线，A,B是切点，点C为 ⊙ O上一点，若 ∠ACB = 70°，则∠P的度数为____ ． 解答题，第一题8分，第二题10分，第三题10分","options":[],"answer":"40°","solution":"如图所示，连接OA,OB，∵ PA,PB是⊙O的切线，A,B为切点，所以OA⊥PA,OB⊥PB，即∠OAP = ∠OBP = 90°，∵点C为⊙O上一点，∠ACB= 70°，∴∠AOB= 2∠ACB= 140°，在四边形AOBP中，∠P= 360°−∠AOB−∠OAP−∠OBP = 360°−140°−90°−90° = 40°．故答案为：40°．","stem_html":"<div>如图所示，PA,PB是 ⊙ O的切线，A,B是切点，点C为 ⊙ O上一点，若 ∠ACB = 70°，则∠P的度数为____ ． 解答题，第一题8分，第二题10分，第三题10分<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/3ed63e64-0697-4d66-84a9-5778adf3f5b0/2d1c946745a7.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"40°","solution_html":"如图所示，连接OA,OB，∵ PA,PB是⊙O的切线，A,B为切点，所以OA⊥PA,OB⊥PB，即∠OAP = ∠OBP = 90°，∵点C为⊙O上一点，∠ACB= 70°，∴∠AOB= 2∠ACB= 140°，在四边形AOBP中，∠P= 360°−∠AOB−∠OAP−∠OBP = 360°−140°−90°−90° = 40°．故答案为：40°．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:05:22"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:05:22"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:05:22"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T08:05:46"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T08:06:20"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:06:20"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T08:06:20"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T08:07:01"},{"type":"QUALITY_GATE","status":"FAIL","score":0.967,"created_at":"2026-09-26T08:07:01"}],"detail_url":"/questions/25243","edit_url":"/questions/25243/edit","json_url":"/api/questions/25243","recheck_url":"/api/questions/25243/recheck"},{"id":25240,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1435.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"下列命题：①三点确定一个圆；②正多边形是中心对称图形；③正六 边形的半径与边长相等；④三角形的外心到三角形各边的距离相等，其中真命题的个数是( ). A. \\(\\frac{4}{3}\\) B. C. 2 D. 1","options":[{"label":"A","text":"\\frac{4}{3}"},{"label":"B","text":""},{"label":"C","text":"2"},{"label":"D","text":"1"}],"answer":"D","solution":"因为①不共线的三个点确定一个圆，故些项为假命题，不符合题意 ；②正三角形是轴对称图形，但不是中心对称图形，故此项是假 命题，不符合题意；③正六边形的半径与边长相等，故此项是真 命题，符合题意；④三角形的外心到三角形三个顶点的距离相等 ，故此项为假命题，不符合题意．真命题有1个，故选：D．","stem_html":"<div>下列命题：①三点确定一个圆；②正多边形是中心对称图形；③正六 边形的半径与边长相等；④三角形的外心到三角形各边的距离相等，其中真命题的个数是(  ).<br>A. \\(\\frac{4}{3}\\)<br>B. <br>C. 2<br>D. 1</div>","answer_html":"D","solution_html":"因为①不共线的三个点确定一个圆，故些项为假命题，不符合题意 ；②正三角形是轴对称图形，但不是中心对称图形，故此项是假 命题，不符合题意；③正六边形的半径与边长相等，故此项是真 命题，符合题意；④三角形的外心到三角形三个顶点的距离相等 ，故此项为假命题，不符合题意．真命题有1个，故选：D．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:00:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T08:00:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T08:00:17"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T08:00:42"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T08:00:43"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T08:00:43"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T08:00:43"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T08:01:02"},{"type":"QUALITY_GATE","status":"PASS","score":0.925,"created_at":"2026-09-26T08:01:02"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/25240","edit_url":"/questions/25240/edit","json_url":"/api/questions/25240","recheck_url":"/api/questions/25240/recheck"},{"id":25230,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1430.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图所示, AB, BC, CD分别与⊙O相切于点E, F, G, 且AB ∥CD, 连接OB, OC． （1）求证：OB ⊥OC； （2）若\\(OB = 6\\),\\(OC = 8\\)，求\\(CG - BE\\)的值．","options":[],"answer":"","solution":"","stem_html":"<div>如图所示, AB, BC, CD分别与⊙O相切于点E, F, G, 且AB ∥CD, 连接OB, OC．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/18c38aab-de76-4dae-b5f4-5e8f3335ef9e/5a72f22224a1.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）求证：OB ⊥OC；<br>（2）若\\(OB = 6\\),\\(OC = 8\\)，求\\(CG - BE\\)的值．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:51:19"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:51:19"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:51:19"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:51:59"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:53:59"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:53:59"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:53:59"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:54:35"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T07:54:35"}],"detail_url":"/questions/25230","edit_url":"/questions/25230/edit","json_url":"/api/questions/25230","recheck_url":"/api/questions/25230/recheck"},{"id":25231,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1430.pdf","job_source":"人教版.zip","pages":[6,6],"stem":"如图，过\\(\\odot O\\)外一点\\(P\\)作圆的切线\\(PA\\),\\(PB\\)，点\\(A\\),\\(B\\)为切点，\\(AC\\)为直径，设\\(\\angle P = m^{\\circ}\\)，\\(\\angle C = n^{\\circ}\\)，则\\(m\\),\\(n\\)的等量关系为____.","options":[],"answer":"","solution":"","stem_html":"<div>如图，过\\(\\odot O\\)外一点\\(P\\)作圆的切线\\(PA\\),\\(PB\\)，点\\(A\\),\\(B\\)为切点，\\(AC\\)为直径，设\\(\\angle P = m^{\\circ}\\)，\\(\\angle C = n^{\\circ}\\)，则\\(m\\),\\(n\\)的等量关系为____.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/d225ee3a-85da-4ab0-a7b1-294b828128c5/3e9b5587e2d1.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:52:32"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:32"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:52:32"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T07:52:48"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T07:57:24"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:57:24"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:57:24"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:57:32"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T07:57:32"}],"detail_url":"/questions/25231","edit_url":"/questions/25231/edit","json_url":"/api/questions/25231","recheck_url":"/api/questions/25231/recheck"},{"id":25222,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.962,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1430.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图， 是正方形ABCD的外接圆若正,\\(\\frac{O}{ABCD}\\)方形 的边长为4,则正方形外接圆的 半径是( ) A .4 .2 .22\\(.4\\sqrt{2}\\)B C D","options":[],"answer":"C","solution":"正方形ABCD的边长为4，其对角线长为\\(\\sqrt{4^2+4^2}=4\\sqrt{2}\\)。因为正方形的对角线是其外接圆的直径，所以外接圆的半径为\\(\\frac{1}{2}\\times4\\sqrt{2}=2\\sqrt{2}\\)。故选C。","stem_html":"<div>如图， 是正方形ABCD的外接圆若正,\\(\\frac{O}{ABCD}\\)方形 的边长为4,则正方形外接圆的 半径是( ) A .4 .2 .22\\(.4\\sqrt{2}\\)B C D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/b0017322-3e26-4c70-943c-c880e5b20859/04a277e07eb9.png\" style=\"width:140.0px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"C","solution_html":"正方形ABCD的边长为4，其对角线长为\\(\\sqrt{4^2+4^2}=4\\sqrt{2}\\)。因为正方形的对角线是其外接圆的直径，所以外接圆的半径为\\(\\frac{1}{2}\\times4\\sqrt{2}=2\\sqrt{2}\\)。故选C。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:49:25"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:49:25"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:49:25"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:49:40"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:49:40"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:49:59"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:49:59"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T07:51:31"},{"type":"QUALITY_GATE","status":"FAIL","score":0.962,"created_at":"2026-09-26T07:51:31"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:40"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:40"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:53"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:53"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:53"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:53"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T07:53:24"}],"detail_url":"/questions/25222","edit_url":"/questions/25222/edit","json_url":"/api/questions/25222","recheck_url":"/api/questions/25222/recheck"},{"id":25229,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.967,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1430.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，正六边形ABCDEF内接于⊙O，⊙O的半径为3，则AB的长为( ).\\(\\frac{(A)2}{(B)3}\\) C. √3 D. 2√3","options":[{"label":"C","text":"√3"},{"label":"D","text":"2√3"}],"answer":"","solution":"","stem_html":"<div>如图，正六边形ABCDEF内接于⊙O，⊙O的半径为3，则AB的长为( ).\\(\\frac{(A)2}{(B)3}\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/85012c65-6d07-4c73-9e15-d68900c113ec/d389c96e9095.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>C. √3<br>D. 2√3</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:52:06"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:06"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:52:06"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:52:27"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T07:52:52"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:52:52"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:52:52"},{"type":"COHERENCE","status":"FAIL","score":1.0,"created_at":"2026-09-26T07:53:00"},{"type":"QUALITY_GATE","status":"FAIL","score":0.967,"created_at":"2026-09-26T07:53:00"}],"detail_url":"/questions/25229","edit_url":"/questions/25229/edit","json_url":"/api/questions/25229","recheck_url":"/api/questions/25229/recheck"},{"id":25227,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1430.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，正方形ABCD的边长为6，且顶点A, B, C, D都在⊙O上，则⊙O的半径为( ).\\(\\frac{(A)3}{(B)6}\\) C. 3√2 D. 6√2","options":[{"label":"C","text":"3√2"},{"label":"D","text":"6√2"}],"answer":"","solution":"","stem_html":"<div>如图，正方形ABCD的边长为6，且顶点A, B, C, D都在⊙O上，则⊙O的半径为( ).\\(\\frac{(A)3}{(B)6}\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/5e3e3d51-808f-4a7d-a23b-b91f6130aa0c/e6a1f8ba65d8.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>C. 3√2<br>D. 6√2</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:49:58"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:49:58"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:49:58"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:50:43"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:50:43"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T07:50:52"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:50:52"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:51:12"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-09-26T07:51:12"}],"detail_url":"/questions/25227","edit_url":"/questions/25227/edit","json_url":"/api/questions/25227","recheck_url":"/api/questions/25227/recheck"},{"id":25218,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1430.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"正六边形的中心角=___________ 的距离，简称_____","options":[],"answer":"60°等边三角形","solution":"依据《核心知识点》第5条：正六边形的中心角=60°等边三角形。","stem_html":"<div>正六边形的中心角=___________ 的距离，简称_____</div>","answer_html":"60°等边三角形","solution_html":"依据《核心知识点》第5条：正六边形的中心角=60°等边三角形。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:45:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:45:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:45:34"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:45:40"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:45:40"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T07:46:08"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:46:08"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:46:50"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:46:50"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T07:48:08"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T07:48:08"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:48:50"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T07:48:50"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T07:48:50"}],"detail_url":"/questions/25218","edit_url":"/questions/25218/edit","json_url":"/api/questions/25218","recheck_url":"/api/questions/25218/recheck"},{"id":25219,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.825,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1430.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"正六边形的外接圆半径与正六边形的边长构成","options":[],"answer":"相等","solution":"正六边形可分割为6个全等的等边三角形，每个三角形的顶点是正六边形的中心与相邻两个顶点。因此，外接圆半径（中心到顶点的距离）等于等边三角形的边长，即正六边形的边长。","stem_html":"<div>正六边形的外接圆半径与正六边形的边长构成</div>","answer_html":"相等","solution_html":"正六边形可分割为6个全等的等边三角形，每个三角形的顶点是正六边形的中心与相邻两个顶点。因此，外接圆半径（中心到顶点的距离）等于等边三角形的边长，即正六边形的边长。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:46:05"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:46:05"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:46:05"},{"type":"VISION","status":"FAIL","score":0.5,"created_at":"2026-09-26T07:46:25"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:46:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:46:38"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:46:38"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:46:48"},{"type":"QUALITY_GATE","status":"FAIL","score":0.825,"created_at":"2026-09-26T07:46:48"}],"detail_url":"/questions/25219","edit_url":"/questions/25219/edit","json_url":"/api/questions/25219","recheck_url":"/api/questions/25219/recheck"},{"id":25207,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1430.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"正六边形的外接圆半径与正六边形的边长构成","options":[],"answer":"等边三角形","solution":"正六边形可分割为6个全等的等腰三角形，其顶角（中心角）为360°/6=60°。由于正六边形各边相等，这些等腰三角形的两腰（即外接圆半径）相等，且底角也相等。根据三角形内角和为180°，每个底角为(180°-60°)/2=60°，因此三个角均为60°，故为正三角形（等边三角形）。","stem_html":"<div>正六边形的外接圆半径与正六边形的边长构成</div>","answer_html":"等边三角形","solution_html":"正六边形可分割为6个全等的等腰三角形，其顶角（中心角）为360°/6=60°。由于正六边形各边相等，这些等腰三角形的两腰（即外接圆半径）相等，且底角也相等。根据三角形内角和为180°，每个底角为(180°-60°)/2=60°，因此三个角均为60°，故为正三角形（等边三角形）。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:43:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:43:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:43:34"},{"type":"VISION","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:43:43"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T07:44:33"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:44:33"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:44:33"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:44:39"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T07:44:39"}],"detail_url":"/questions/25207","edit_url":"/questions/25207/edit","json_url":"/api/questions/25207","recheck_url":"/api/questions/25207/recheck"},{"id":25194,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1425.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图所示, 直线AB、BC、CD分别与⊙O相切于E、F、G, 且AB ∥CD, OB=5cm, OC = 12cm. 求: （1）∠BOC的度数; （2）BE + CG的长; （3）⊙O的半径.","options":[],"answer":"","solution":"","stem_html":"<div>如图所示, 直线AB、BC、CD分别与⊙O相切于E、F、G, 且AB ∥CD, OB=5cm, OC = 12cm. 求:<br>（1）∠BOC的度数;<br>（2）BE + CG的长;<br>（3）⊙O的半径.</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:39:09"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:39:09"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:39:09"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T07:39:35"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:39:41"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:39:41"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:39:41"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:39:55"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T07:39:55"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:42:12"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:42:12"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:42:44"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T07:42:44"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T07:42:44"}],"detail_url":"/questions/25194","edit_url":"/questions/25194/edit","json_url":"/api/questions/25194","recheck_url":"/api/questions/25194/recheck"},{"id":25195,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1425.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图所示，PA、PB是⊙O的两条切线，C在⊙O上，∠APB = 78°，则∠ACB = ____°．","options":[],"answer":"","solution":"","stem_html":"<div>如图所示，PA、PB是⊙O的两条切线，C在⊙O上，∠APB = 78°，则∠ACB = ____°．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/1778b3a1-d051-4f61-8828-8f2855f062f1/cb9734ce0db1.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:37:49"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:37:49"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:37:49"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:37:58"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T07:40:19"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T07:40:19"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:40:19"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:40:22"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T07:40:22"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T07:40:37"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T07:40:37"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:41:41"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:41:41"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:41:41"}],"detail_url":"/questions/25195","edit_url":"/questions/25195/edit","json_url":"/api/questions/25195","recheck_url":"/api/questions/25195/recheck"},{"id":25184,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"SENIOR","subject_stage":"数学·高中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1425.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"正n边形的外角和为_____，每一个外角的度","options":[],"answer":"360°；360°/n","solution":"多边形外角和定理：任意凸n边形的外角和恒为360°。对于正n边形，由于n个外角相等，每个外角的度数为360°除以n，即360°/n。","stem_html":"<div>正n边形的外角和为_____，每一个外角的度</div>","answer_html":"360°；360°/n","solution_html":"多边形外角和定理：任意凸n边形的外角和恒为360°。对于正n边形，由于n个外角相等，每个外角的度数为360°除以n，即360°/n。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:34:55"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:34:55"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:34:55"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:35:17"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:35:17"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:36:00"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:36:00"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T07:36:12"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T07:36:12"}],"detail_url":"/questions/25184","edit_url":"/questions/25184/edit","json_url":"/api/questions/25184","recheck_url":"/api/questions/25184/recheck"},{"id":25155,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图所示，PA、PB是⊙O的两条切线，C在⊙O上，∠APB = 78°，则∠ACB = ____°．","options":[],"answer":"","solution":"","stem_html":"<div>如图所示，PA、PB是⊙O的两条切线，C在⊙O上，∠APB = 78°，则∠ACB = ____°．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:22:52"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:22:52"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:22:52"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:23:01"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T07:28:36"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:28:36"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:28:36"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:28:41"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T07:28:41"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T07:29:34"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T07:29:34"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:31:02"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:31:02"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:31:02"}],"detail_url":"/questions/25155","edit_url":"/questions/25155/edit","json_url":"/api/questions/25155","recheck_url":"/api/questions/25155/recheck"},{"id":25156,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图所示，PA、PB分别与⊙O相切于A、B两点．若∠C = 70°，则∠P的度数为( ). A. 70° B. 55° C. 50° D. 40°","options":[{"label":"A","text":"70°"},{"label":"B","text":"55°"},{"label":"C","text":"50°"},{"label":"D","text":"40°"}],"answer":"","solution":"","stem_html":"<div>如图所示，PA、PB分别与⊙O相切于A、B两点．若∠C = 70°，则∠P的度数为( ).<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/1822ac80-752c-4172-987c-a22fd1d30f6e/0e56ac8c4383.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 70°<br>B. 55°<br>C. 50°<br>D. 40°</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:23:12"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:23:12"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:23:12"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:24:05"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:24:10"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:24:10"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:24:10"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:24:36"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T07:24:36"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T07:26:37"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T07:26:37"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:29:04"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:29:04"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T07:29:04"}],"detail_url":"/questions/25156","edit_url":"/questions/25156/edit","json_url":"/api/questions/25156","recheck_url":"/api/questions/25156/recheck"},{"id":25151,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"[小试1] 如图所示，直线AB、BC、CD分别与⊙O相切于点E、F、G，且AB ∥ CD，若OB = 8cm，OC = 6cm，则BE + CG等于( ). A. 7cm\\(\\frac{(B)8cm}{(C)9cm}\\) D. 10cm","options":[{"label":"A","text":"7cm \\frac{(B)8cm}{(C)9cm}"},{"label":"D","text":"10cm"}],"answer":"D","solution":"连接OF, 根据切线长定理得: BE = BF, CF = CG, ∠OBF = ∠OBE, ∠OCF=∠OCG. ∵AB ∥CD, ∴∠ABC + ∠BCD = 180∘, ∴∠OBF + ∠OCF = 90°,所以∠BOC = 90°, ∵OB = 6cm, , OC = 8cm, ∴BC =\\(\\sqrt{OB^{2}}\\)+\\(OC^{2}\\)=\\(\\sqrt{8^{2}}\\)+\\(6^{2}\\)= 10(cm), ∵OF ⊥BC. ∴BE = BF, CG = CF, ∴BE + CG=BF + CF = BC = 10(cm). 故选D. 2.80 ⏜ 如图所示，连接 OB, ∵AB所对圆周角是∠C，所对圆心角是∠AOB,所以∠AOB = 2∠C = 100°， ∵ PA、PB分别切⊙O于点A、B, ∴∠PAO=∠PBO = 90°, 在四边形APBO中, ∠P = 360° −∠PAO − ∠PBO −∠AOB=360° −90° −90° −100° = 80°，故答案为：80．","stem_html":"<div>[小试1] 如图所示，直线AB、BC、CD分别与⊙O相切于点E、F、G，且AB ∥ CD，若OB = 8cm，OC = 6cm，则BE + CG等于( ).<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/b1aeac6c-c16f-4882-af6a-ced20e9fe6e9/d42583485990.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 7cm\\(\\frac{(B)8cm}{(C)9cm}\\)<br>D. 10cm</div>","answer_html":"D","solution_html":"连接OF, 根据切线长定理得: BE = BF, CF = CG, ∠OBF = ∠OBE, ∠OCF=∠OCG. ∵AB ∥CD, ∴∠ABC + ∠BCD = 180∘, ∴∠OBF + ∠OCF = 90°,所以∠BOC = 90°, ∵OB = 6cm, , OC = 8cm, ∴BC =\\(\\sqrt{OB^{2}}\\)+\\(OC^{2}\\)=\\(\\sqrt{8^{2}}\\)+\\(6^{2}\\)= 10(cm), ∵OF ⊥BC. ∴BE = BF, CG = CF, ∴BE + CG=BF + CF = BC = 10(cm). 故选D. 2.80 ⏜ 如图所示，连接 OB, ∵AB所对圆周角是∠C，所对圆心角是∠AOB,所以∠AOB = 2∠C = 100°， ∵ PA、PB分别切⊙O于点A、B, ∴∠PAO=∠PBO = 90°, 在四边形APBO中, ∠P = 360° −∠PAO − ∠PBO −∠AOB=360° −90° −90° −100° = 80°，故答案为：80．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:25:35"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:25:35"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:25:35"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T07:26:12"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T07:28:24"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:28:24"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:28:24"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:28:39"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T07:28:39"}],"detail_url":"/questions/25151","edit_url":"/questions/25151/edit","json_url":"/api/questions/25151","recheck_url":"/api/questions/25151/recheck"},{"id":25154,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图所示，AB, BC, CD分别与⊙O相切于E, F, G三点，若AB ∥CD, OB=\\(3\\mathrm{cm}\\)OC =\\(6\\mathrm{cm}\\)则线段BE + CG的值为___\\(\\mathrm{cm}\\).","options":[],"answer":"","solution":"","stem_html":"<div>如图所示，AB, BC, CD分别与⊙O相切于E, F, G三点，若AB ∥CD, OB=\\(3\\mathrm{cm}\\)OC =\\(6\\mathrm{cm}\\)则线段BE + CG的值为___\\(\\mathrm{cm}\\).<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/0d431059-de46-4855-b721-6cd4a55b52f4/346f4d3e4f61.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:22:21"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:22:21"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:22:21"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T07:23:07"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T07:26:15"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:26:15"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:26:15"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:26:37"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:26:37"}],"detail_url":"/questions/25154","edit_url":"/questions/25154/edit","json_url":"/api/questions/25154","recheck_url":"/api/questions/25154/recheck"},{"id":25152,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"[小试2] 如图，PA, PB分别与⊙O相切于点A, B. 若∠P = 36°，则∠ACB小为___°.","options":[],"answer":"","solution":"","stem_html":"<div>[小试2] 如图，PA, PB分别与⊙O相切于点A, B. 若∠P = 36°，则∠ACB小为___°.</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:20:45"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:20:45"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:20:45"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T07:21:26"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T07:21:26"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T07:21:34"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:21:34"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:21:48"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:21:48"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T07:25:29"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T07:25:29"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:26:32"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:26:32"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:26:32"}],"detail_url":"/questions/25152","edit_url":"/questions/25152/edit","json_url":"/api/questions/25152","recheck_url":"/api/questions/25152/recheck"},{"id":25149,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"\\(\\frac{如图}{FG} \\frac{ABBCCD}{ABCDOB}\\),,, 分别与 O相切于点, E ,,且 , = 6,OC = 求 的度数；\\(\\frac{(1)}{(2)} \\frac{BOC}{O}\\)求  的半径.","options":[],"answer":"","solution":"(1),, 分别与 O 相切，\\(\\frac{ABBCCD}{ABCOC}\\)OB平分, 平分BCD. ,\\(\\frac{ABCD}{ABC}\\) +  = 180,\\(\\frac{BCD}{OCB} (ABC + BCD)\\) +  = = 90,\\(\\frac{OBC}{BOC} 2\\) = − = \\(\\frac{180}{OF} \\frac{90}{BC} 90\\). (2)过点作O ⊥ 于, F 则OF 为  O.\\(\\frac{的半径}{OB}\\)在 RtBOC 中, = 6,OC = 8,  BC =\\(\\sqrt{(6^{2}+8^{2})} = 1 0\\). 由面积法:SBOC =\\(\\frac{1}{2}\\) OB  OC =\\(\\frac{1}{2}\\) BC  OF, 即\\(\\frac{1}{2}\\) =\\(\\frac{1}{2}\\)10 OF,\\(\\frac{68}{OF}\\)解得 = 4.8, 即 O 的半径为4.8.","stem_html":"<div>\\(\\frac{如图}{FG} \\frac{ABBCCD}{ABCDOB}\\),,, 分别与 O相切于点, E ,,且 , = 6,OC = 求 的度数；\\(\\frac{(1)}{(2)} \\frac{BOC}{O}\\)求  的半径.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/5c907702-1232-4103-bc8e-2822a5ac2998/095e361cf55c.png\" style=\"width:98.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"(1),, 分别与 O 相切，\\(\\frac{ABBCCD}{ABCOC}\\)OB平分, 平分BCD. ,\\(\\frac{ABCD}{ABC}\\) +  = 180,\\(\\frac{BCD}{OCB} (ABC + BCD)\\) +  = = 90,\\(\\frac{OBC}{BOC} 2\\) = − = \\(\\frac{180}{OF} \\frac{90}{BC} 90\\). (2)过点作O ⊥ 于, F 则OF 为  O.\\(\\frac{的半径}{OB}\\)在 RtBOC 中, = 6,OC = 8,  BC =\\(\\sqrt{(6^{2}+8^{2})} = 1 0\\). 由面积法:SBOC =\\(\\frac{1}{2}\\) OB  OC =\\(\\frac{1}{2}\\) BC  OF, 即\\(\\frac{1}{2}\\) =\\(\\frac{1}{2}\\)10 OF,\\(\\frac{68}{OF}\\)解得 = 4.8, 即 O 的半径为4.8.","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:24:23"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:24:23"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:24:23"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T07:24:44"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:25:28"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:25:28"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:25:28"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:26:14"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-09-26T07:26:14"}],"detail_url":"/questions/25149","edit_url":"/questions/25149/edit","json_url":"/api/questions/25149","recheck_url":"/api/questions/25149/recheck"},{"id":25148,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.775,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"求与圆相切的三角形或四边形的周长：","options":[],"answer":"利用切线长定理进行转化","solution":"根据《核心知识点》第6条，求与圆相切的三角形或四边形的周长，需要利用切线长定理进行转化。","stem_html":"<div>求与圆相切的三角形或四边形的周长：</div>","answer_html":"利用切线长定理进行转化","solution_html":"根据《核心知识点》第6条，求与圆相切的三角形或四边形的周长，需要利用切线长定理进行转化。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:19:43"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:19:43"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:19:43"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T07:19:58"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T07:19:58"},{"type":"VISION","status":"FAIL","score":0.5,"created_at":"2026-09-26T07:20:21"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:20:21"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:20:35"},{"type":"QUALITY_GATE","status":"FAIL","score":0.775,"created_at":"2026-09-26T07:20:35"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T07:21:54"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:21:54"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:22:09"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:22:09"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:22:09"}],"detail_url":"/questions/25148","edit_url":"/questions/25148/edit","json_url":"/api/questions/25148","recheck_url":"/api/questions/25148/recheck"},{"id":25140,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.863,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"求与圆相切的三角形或四边形的周长： _________________________________________","options":[],"answer":"利用切线长定理，将各边转化为从顶点到切点的线段长之和","solution":"根据核心知识点第2条“从圆外一点引圆的两条切线，切线长相等”，可将三角形或四边形的各边分解为从顶点到切点的线段，通过等量代换求和得到周长","stem_html":"<div>求与圆相切的三角形或四边形的周长： _________________________________________</div>","answer_html":"利用切线长定理，将各边转化为从顶点到切点的线段长之和","solution_html":"根据核心知识点第2条“从圆外一点引圆的两条切线，切线长相等”，可将三角形或四边形的各边分解为从顶点到切点的线段，通过等量代换求和得到周长","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:17:46"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:17:46"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:17:46"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T07:18:05"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T07:18:05"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:18:37"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:18:37"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:19:03"},{"type":"QUALITY_GATE","status":"FAIL","score":0.863,"created_at":"2026-09-26T07:19:03"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T07:22:02"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T07:22:02"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:22:02"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T07:22:02"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:22:02"}],"detail_url":"/questions/25140","edit_url":"/questions/25140/edit","json_url":"/api/questions/25140","recheck_url":"/api/questions/25140/recheck"},{"id":25146,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.688,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"求与圆相切的三角形或四边形的周长： _________________________________________","options":[],"answer":"利用切线长定理，将各边转化为从顶点到切点的线段长之和，再通过已知条件（如半径、角度、其他边长等）建立方程求解","solution":"","stem_html":"<div>求与圆相切的三角形或四边形的周长： _________________________________________</div>","answer_html":"利用切线长定理，将各边转化为从顶点到切点的线段长之和，再通过已知条件（如半径、角度、其他边长等）建立方程求解","solution_html":"","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:19:03"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:19:03"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:19:03"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T07:19:34"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T07:19:34"},{"type":"VISION","status":"FAIL","score":0.0,"created_at":"2026-09-26T07:19:55"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:19:55"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:20:15"},{"type":"QUALITY_GATE","status":"FAIL","score":0.688,"created_at":"2026-09-26T07:20:15"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T07:21:27"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T07:21:27"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:21:27"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T07:21:27"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:21:27"}],"detail_url":"/questions/25146","edit_url":"/questions/25146/edit","json_url":"/api/questions/25146","recheck_url":"/api/questions/25146/recheck"},{"id":25134,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.675,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1420.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"求与圆相切的三角形或四边形的周长： _________________________________________","options":[],"answer":"利用切线长定理将各边转化为与圆相切的线段之和","solution":"","stem_html":"<div>求与圆相切的三角形或四边形的周长： _________________________________________</div>","answer_html":"利用切线长定理将各边转化为与圆相切的线段之和","solution_html":"","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:16:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:16:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:16:34"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T07:16:46"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T07:16:46"},{"type":"VISION","status":"FAIL","score":0.0,"created_at":"2026-09-26T07:17:16"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:17:16"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:17:38"},{"type":"QUALITY_GATE","status":"FAIL","score":0.675,"created_at":"2026-09-26T07:17:38"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T07:19:03"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T07:19:03"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:19:03"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T07:19:03"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.8,"created_at":"2026-09-26T07:19:03"}],"detail_url":"/questions/25134","edit_url":"/questions/25134/edit","json_url":"/api/questions/25134","recheck_url":"/api/questions/25134/recheck"},{"id":25117,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.967,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1415.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图,P是 ⊙ O外一点,PA,PB分别和 ⊙ O切于A、 B,C是弧AB上任意一点,过 C作⊙O的切线分别交PA, PB于D 、E, 若△PDE的周长为20cm, 则PA长为____ ． 解答题，第一题8分，第二题10分，第三题10分","options":[],"answer":"10cm/10厘米","solution":"因为PA,PB分别和 ⊙ O切于A、 B， ∴ PA=PB， ∵ 过C作 ⊙ O的切线分别交 PA,PB于D,E， ∴ DA=DC,EB=EC ∵△ PDE的周长为20cm， ∴ PD+DE+ PE = 20cm， ∴ PD+DC+EC+PE = 20cm， ∴ PD+DA+EB+PE = 20cm,则 PA + PB = 20cm，∴2PA = 20cm, 即PA = 10cm. 故答案为10cm．","stem_html":"<div>如图,P是 ⊙ O外一点,PA,PB分别和 ⊙ O切于A、 B,C是弧AB上任意一点,过 C作⊙O的切线分别交PA, PB于D 、E, 若△PDE的周长为20cm, 则PA长为____ ． 解答题，第一题8分，第二题10分，第三题10分<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/0df0f8de-9e2f-4e72-abc1-df12ac4669d7/9c4c4c55e830.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"10cm/10厘米","solution_html":"因为PA,PB分别和 ⊙ O切于A、 B， ∴ PA=PB， ∵ 过C作 ⊙ O的切线分别交 PA,PB于D,E， ∴ DA=DC,EB=EC ∵△ PDE的周长为20cm， ∴ PD+DE+ PE = 20cm， ∴ PD+DC+EC+PE = 20cm， ∴ PD+DA+EB+PE = 20cm,则 PA + PB = 20cm，∴2PA = 20cm, 即PA = 10cm. 故答案为10cm．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:09:24"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:09:24"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:09:24"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:09:54"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T07:10:09"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:10:09"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:10:09"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T07:10:22"},{"type":"QUALITY_GATE","status":"FAIL","score":0.967,"created_at":"2026-09-26T07:10:22"}],"detail_url":"/questions/25117","edit_url":"/questions/25117/edit","json_url":"/api/questions/25117","recheck_url":"/api/questions/25117/recheck"},{"id":25113,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1415.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，\\(\\triangle ABC\\)的内切圆\\(\\odot O\\)与\\(AB\\)、\\(BC\\)、\\(CA\\)分别相切于点\\(D\\)、\\(E\\)、\\(F\\)，且\\(AD=3\\)，\\(\\triangle ABC\\)的周长为24，则\\(BC\\)的长为____．","options":[],"answer":"9","solution":"因为\\(\\triangle ABC\\)的内切圆\\(\\odot O\\)与\\(AB\\)、\\(BC\\)、\\(CA\\)分别相切于点\\(D\\)、\\(E\\)、\\(F\\)，且\\(AD=3\\)，\\therefore\\(AF=AD=3\\)，\\(CF=CE\\)，\\(BD=BE\\)，\\therefore\\(CF+BD=CE+BE=BC\\)，因为\\(\\triangle ABC\\)的周长为 24，\\therefore\\(AF+CF+BC+BD+AD=24\\)，\\therefore\\(3+2BC+3=24\\)，\\therefore\\(BC=9\\)，故答案为：9．","stem_html":"<div>如图，\\(\\triangle ABC\\)的内切圆\\(\\odot O\\)与\\(AB\\)、\\(BC\\)、\\(CA\\)分别相切于点\\(D\\)、\\(E\\)、\\(F\\)，且\\(AD=3\\)，\\(\\triangle ABC\\)的周长为24，则\\(BC\\)的长为____．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/53d2a1ed-c0ef-492a-9b03-96c687b41538/a429d846e5ae.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"9","solution_html":"因为\\(\\triangle ABC\\)的内切圆\\(\\odot O\\)与\\(AB\\)、\\(BC\\)、\\(CA\\)分别相切于点\\(D\\)、\\(E\\)、\\(F\\)，且\\(AD=3\\)，\\therefore\\(AF=AD=3\\)，\\(CF=CE\\)，\\(BD=BE\\)，\\therefore\\(CF+BD=CE+BE=BC\\)，因为\\(\\triangle ABC\\)的周长为 24，\\therefore\\(AF+CF+BC+BD+AD=24\\)，\\therefore\\(3+2BC+3=24\\)，\\therefore\\(BC=9\\)，故答案为：9．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:02:02"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:02"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:02:02"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:17"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:57"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:57"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:57"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:04:24"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T07:04:24"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:32"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:32"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T07:09:05"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:09:05"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T07:09:05"}],"detail_url":"/questions/25113","edit_url":"/questions/25113/edit","json_url":"/api/questions/25113","recheck_url":"/api/questions/25113/recheck"},{"id":25115,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1415.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，I是△ABC的内心，∠A = 56°，则∠BIC=____ °．","options":[],"answer":"112","solution":"I是△ABC的内心，故BI、CI分别平分∠ABC和∠ACB。在△BIC中，∠BIC = 180° - (∠IBC + ∠ICB) = 180° - ½(∠ABC + ∠ACB)。又∠ABC + ∠ACB = 180° - ∠A = 124°，因此∠BIC = 180° - 62° = 112°。","stem_html":"<div>如图，I是△ABC的内心，∠A = 56°，则∠BIC=____ °．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/bd65524c-9862-4ed6-9d56-0a39ff331b18/510e29804e79.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"112","solution_html":"I是△ABC的内心，故BI、CI分别平分∠ABC和∠ACB。在△BIC中，∠BIC = 180° - (∠IBC + ∠ICB) = 180° - ½(∠ABC + ∠ACB)。又∠ABC + ∠ACB = 180° - ∠A = 124°，因此∠BIC = 180° - 62° = 112°。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:04:40"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:04:40"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:04:40"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:12"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:18"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:18"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:18"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:05:28"},{"type":"QUALITY_GATE","status":"PASS","score":0.95,"created_at":"2026-09-26T07:05:28"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:51"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:51"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:51"},{"type":"AUTO_FILL_ANSWER","status":"WARN","score":1.0,"created_at":"2026-09-26T07:05:51"},{"type":"VISION","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:06:29"}],"detail_url":"/questions/25115","edit_url":"/questions/25115/edit","json_url":"/api/questions/25115","recheck_url":"/api/questions/25115/recheck"},{"id":25111,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.975,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1415.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图， △ ABC的内切圆 ⊙ O与BC,CA,AB分别相切于点D,E,F,且AB= 9,BC= 14, CA = 13, 则AF的长为( ) A. \\(\\frac{3}{4}\\) B. C. 6 D. 8 填空题，每题6分","options":[{"label":"A","text":"\\frac{3}{4}"},{"label":"B","text":""},{"label":"C","text":"6"},{"label":"D","text":"8 填空题，每题6分"}],"answer":"B","solution":"因为 △ ABC的内切圆 ⊙ O与BC,CA,AB分别相切于点D,E,F， ∴ AE =AF,BD= BF,CD=CE,设AE =AF =a,BD=BF =b,CD=CE =c,∵ AB= 9,BC= ⎧⎪ a+b= 9 ⎧⎪ a= 4 14,CA= 13， ∴⎨ a+c= 13,解得⎨ b= 5,∴ AF = 4,故选 :B． ⎩⎪ ⎩⎪ b+c= 14 c= 9","stem_html":"<div>如图， △ ABC的内切圆 ⊙ O与BC,CA,AB分别相切于点D,E,F,且AB= 9,BC= 14, CA = 13, 则AF的长为(      )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/3eaa7dd2-7cd5-438d-9aeb-e8f55669f65e/72da01c8f8cb.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. \\(\\frac{3}{4}\\)<br>B. <br>C. 6<br>D. 8 填空题，每题6分</div>","answer_html":"B","solution_html":"因为 △ ABC的内切圆 ⊙ O与BC,CA,AB分别相切于点D,E,F， ∴ AE =AF,BD= BF,CD=CE,设AE =AF =a,BD=BF =b,CD=CE =c,∵ AB= 9,BC= ⎧⎪ a+b= 9 ⎧⎪ a= 4 14,CA= 13， ∴⎨ a+c= 13,解得⎨ b= 5,∴ AF = 4,故选 :B． ⎩⎪ ⎩⎪ b+c= 14 c= 9","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:02:32"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:32"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:02:32"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:59"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:04:27"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:04:27"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:04:27"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T07:05:23"},{"type":"QUALITY_GATE","status":"PASS","score":0.975,"created_at":"2026-09-26T07:05:23"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/25111","edit_url":"/questions/25111/edit","json_url":"/api/questions/25111","recheck_url":"/api/questions/25111/recheck"},{"id":25110,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.963,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1415.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图,正三角形的内切圆半径为1,那么这个正三角形的边长为( ) A. 2√3 B. \\(\\frac{3}{1}\\) C. D. 2","options":[{"label":"A","text":"2√3"},{"label":"B","text":"\\frac{3}{1}"},{"label":"C","text":""},{"label":"D","text":"2"}],"answer":"A","solution":"过O点作OD ⊥AB, 则OD = 1．∵O是△ABC的内心，∴∠OAD = 30∘; Rt △OAD中 ∠OAD = 30∘, OD = 1，∴OA = 2, ∴AD =\\(\\sqrt{OA^{2}}\\)−\\(OD^{2}\\)=\\(\\sqrt{2^{2}}\\)−\\(1^{2}\\)= √3,即 AB = 2AD = 2√3. 故选: A．","stem_html":"<div>如图,正三角形的内切圆半径为1,那么这个正三角形的边长为(      )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/4e9b98b9-83ec-4a7a-b1b5-7019baa4e235/6c3de6b1b2aa.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 2√3<br>B. \\(\\frac{3}{1}\\)<br>C. <br>D. 2</div>","answer_html":"A","solution_html":"过O点作OD ⊥AB, 则OD = 1．∵O是△ABC的内心，∴∠OAD = 30∘;  Rt △OAD中 ∠OAD = 30∘, OD = 1，∴OA = 2, ∴AD =\\(\\sqrt{OA^{2}}\\)−\\(OD^{2}\\)=\\(\\sqrt{2^{2}}\\)−\\(1^{2}\\)= √3,即 AB = 2AD = 2√3. 故选: A．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:02:12"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:12"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:02:12"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:40"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:40"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T07:02:49"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T07:02:49"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T07:04:09"},{"type":"QUALITY_GATE","status":"PASS","score":0.963,"created_at":"2026-09-26T07:04:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/25110","edit_url":"/questions/25110/edit","json_url":"/api/questions/25110","recheck_url":"/api/questions/25110/recheck"},{"id":25107,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1415.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"如图，\\(\\triangle ABC\\)的内切圆\\(\\odot O\\)与\\(AB\\)，\\(BC\\)，\\(CA\\)分别相切于点\\(D\\)，\\(E\\)，\\(F\\)，且\\(AD = 2\\)，\\(BC = 5\\)，则\\(\\triangle ABC\\)的周长为( ) A. 7 B. 10 C. 14 D. 16","options":[{"label":"A","text":"7"},{"label":"B","text":"10"},{"label":"C","text":"14"},{"label":"D","text":"16"}],"answer":"","solution":"","stem_html":"<div>如图，\\(\\triangle ABC\\)的内切圆\\(\\odot O\\)与\\(AB\\)，\\(BC\\)，\\(CA\\)分别相切于点\\(D\\)，\\(E\\)，\\(F\\)，且\\(AD = 2\\)，\\(BC = 5\\)，则\\(\\triangle ABC\\)的周长为(      )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/1a9eeee0-b7ac-4f3d-809f-e2c7fd678d65/8c657741b3eb.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 7<br>B. 10<br>C. 14<br>D. 16</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T07:00:06"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T07:00:06"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T07:00:06"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T07:00:31"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T07:02:00"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:02:00"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T07:02:00"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T07:02:13"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T07:02:13"}],"detail_url":"/questions/25107","edit_url":"/questions/25107/edit","json_url":"/api/questions/25107","recheck_url":"/api/questions/25107/recheck"},{"id":25096,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1410.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图， 与它的内切圆\\(O \\frac{ABC}{DEF} \\frac{分别相切于}{BC} = 6\\)则 点,,.若 ABC的周长为20, AD的长为( ) A .8 .6 .4 .5 B C D","options":[],"answer":"","solution":"ABC 分别与三边相切于,D E, F,\\(\\frac{的内切圆}{ADBD} \\frac{O}{BECE}\\) =, =, =.\\(\\frac{AF}{AD} \\frac{CF}{yCE}\\)设 = = x, BD = BE =, = = z,\\(\\frac{AF}{ABy} \\frac{CF}{AC}\\)则 + y =, + = = 6, x + z =.\\(\\frac{x}{ABC} \\frac{z}{x} \\frac{BC}{y}\\) = 2 + 2 + 2z = 20,\\(\\frac{的周长}{z}\\)即 + + =10,\\(\\frac{x}{x} \\frac{y}{10}\\) = − (y + z) =10 − 6 = 4,即 AD = 故选. 4.","stem_html":"<div>如图， 与它的内切圆\\(O \\frac{ABC}{DEF} \\frac{分别相切于}{BC} = 6\\)则 点,,.若 ABC的周长为20, AD的长为( ) A .8 .6 .4 .5 B C D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/1d6d68a4-c3a1-4af3-8a55-46eb20e97658/56a15a5ec211.png\" style=\"width:131.0px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"ABC 分别与三边相切于,D E, F,\\(\\frac{的内切圆}{ADBD} \\frac{O}{BECE}\\) =, =, =.\\(\\frac{AF}{AD} \\frac{CF}{yCE}\\)设 = = x, BD = BE =, = = z,\\(\\frac{AF}{ABy} \\frac{CF}{AC}\\)则 + y =, + = = 6, x + z =.\\(\\frac{x}{ABC} \\frac{z}{x} \\frac{BC}{y}\\) = 2 + 2 + 2z = 20,\\(\\frac{的周长}{z}\\)即 + + =10,\\(\\frac{x}{x} \\frac{y}{10}\\) = − (y + z) =10 − 6 = 4,即 AD = 故选. 4.","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:53:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:53:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:53:50"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:54:47"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:54:47"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T06:55:07"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:55:07"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:58:53"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-09-26T06:58:53"}],"detail_url":"/questions/25096","edit_url":"/questions/25096/edit","json_url":"/api/questions/25096","recheck_url":"/api/questions/25096/recheck"},{"id":25102,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1410.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"等边三角形的边长为4, 则它的内切圆面积等于( ) A. \\(4\\pi\\) B. \\(4 _{3}\\pi\\) C. 2 D. \\(16 _{3}\\pi _{3}\\pi\\)","options":[{"label":"A","text":"4\\pi"},{"label":"B","text":"4 _{3}\\pi"},{"label":"C","text":"2"},{"label":"D","text":"16 _{3}\\pi _{3}\\pi"}],"answer":"B","solution":"等边三角形边长为4，其内切圆半径r可通过公式r = (√3/6)\\(\\times\\)边长计算，得r = (√3/6)\\(\\times 4 = (2√3)/3\\)。内切圆面积S =\\(\\pi{}r^{2} = \\pi\\times (4\\times 3)/9 = (4\\pi)/3\\)，对应选项B。","stem_html":"<div>等边三角形的边长为4, 则它的内切圆面积等于( )<br>A. \\(4\\pi\\)<br>B. \\(4 _{3}\\pi\\)<br>C. 2<br>D. \\(16 _{3}\\pi _{3}\\pi\\)</div>","answer_html":"B","solution_html":"等边三角形边长为4，其内切圆半径r可通过公式r = (√3/6)\\(\\times\\)边长计算，得r = (√3/6)\\(\\times 4 = (2√3)/3\\)。内切圆面积S =\\(\\pi{}r^{2} = \\pi\\times (4\\times 3)/9 = (4\\pi)/3\\)，对应选项B。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:54:42"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:54:42"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:54:42"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:55:00"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:55:00"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T06:55:06"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:55:06"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:55:32"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T06:55:32"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:56:27"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:56:27"},{"type":"COHERENCE","status":"PASS","score":0.85,"created_at":"2026-09-26T06:57:55"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:57:55"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T06:57:55"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-09-26T06:57:55"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T06:58:08"}],"detail_url":"/questions/25102","edit_url":"/questions/25102/edit","json_url":"/api/questions/25102","recheck_url":"/api/questions/25102/recheck"},{"id":25105,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1410.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，AC，AB，BD是⊙O的切线，切点分别为C，E，D点，若AB = 12，BD=3，则AC的长为____．","options":[],"answer":"","solution":"","stem_html":"<div>如图，AC，AB，BD是⊙O的切线，切点分别为C，E，D点，若AB = 12，BD=3，则AC的长为____．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:52:52"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:52:52"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:52:52"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T06:53:03"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:53:56"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:53:56"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:53:56"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T06:54:16"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:54:16"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:55:01"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:55:01"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T06:56:48"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:56:48"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T06:56:48"}],"detail_url":"/questions/25105","edit_url":"/questions/25105/edit","json_url":"/api/questions/25105","recheck_url":"/api/questions/25105/recheck"},{"id":25098,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1410.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"【小试1】 如图， △ABC 的内切圆 ⊙O 分别与 AB, BC, AC 相切于点 D, E, F, 且AD = 6, BE=4. 若△ABC的周长为36, 则CF的长为____．","options":[],"answer":"","solution":"","stem_html":"<div>【小试1】 如图， △ABC 的内切圆 ⊙O 分别与 AB, BC, AC 相切于点 D, E, F, 且AD = 6, BE=4. 若△ABC的周长为36, 则CF的长为____．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:50:53"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:50:53"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:50:53"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T06:51:08"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:51:20"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:51:20"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:51:20"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:51:36"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T06:51:36"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T06:54:34"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:54:34"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T06:56:06"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:56:06"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T06:56:06"}],"detail_url":"/questions/25098","edit_url":"/questions/25098/edit","json_url":"/api/questions/25098","recheck_url":"/api/questions/25098/recheck"},{"id":25104,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1410.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，PE、PG为⊙O的两条切线，E、G为切点，点F为⊙O上一点. 连接OE、OG、EF、FG，若∠EFG = 52°，则∠P的度数为( ). A. 52∘ B. 56∘ C. 66∘ D. 76∘","options":[{"label":"A","text":"52∘"},{"label":"B","text":"56∘"},{"label":"C","text":"66∘"},{"label":"D","text":"76∘"}],"answer":"","solution":"","stem_html":"<div>如图，PE、PG为⊙O的两条切线，E、G为切点，点F为⊙O上一点. 连接OE、OG、EF、FG，若∠EFG = 52°，则∠P的度数为( ).<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/e1726df2-6a02-4aa1-921c-569fde150361/4f94b12f682e.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 52∘<br>B. 56∘<br>C. 66∘<br>D. 76∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:53:06"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:53:06"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:53:06"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:53:40"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T06:53:47"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:53:47"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:53:47"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:54:26"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T06:54:26"}],"detail_url":"/questions/25104","edit_url":"/questions/25104/edit","json_url":"/api/questions/25104","recheck_url":"/api/questions/25104/recheck"},{"id":25088,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1410.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"从圆外一点引圆的两条切线，切线长_______","options":[],"answer":"相等","solution":"依据切线长定理：从圆外一点引圆的两条切线，它们的切线长相等。","stem_html":"<div>从圆外一点引圆的两条切线，切线长_______</div>","answer_html":"相等","solution_html":"依据切线长定理：从圆外一点引圆的两条切线，它们的切线长相等。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:47:28"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:47:28"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:47:28"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:47:42"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:47:42"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T06:48:43"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:48:43"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T06:49:00"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T06:49:00"}],"detail_url":"/questions/25088","edit_url":"/questions/25088/edit","json_url":"/api/questions/25088","recheck_url":"/api/questions/25088/recheck"},{"id":25074,"job_id":3,"qa_status":"QUARANTINED","question_type":"knowledge","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":1.0,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1410.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"内心到三角形三个顶点的连线分别平分对应的","options":[],"answer":"","solution":"","stem_html":"<div>内心到三角形三个顶点的连线分别平分对应的</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-09-26T06:45:53"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:45:53"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T06:46:44"},{"type":"QUALITY_GATE","status":"FAIL","score":1.0,"created_at":"2026-09-26T06:46:44"}],"detail_url":"/questions/25074","edit_url":"/questions/25074/edit","json_url":"/api/questions/25074","recheck_url":"/api/questions/25074/recheck"},{"id":25070,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，PE、PG为⊙O的两条切线，E、G为切点，点F为⊙O上一点. 连接OE、OG、EF、FG，若∠EFG = 52°, 则∠P的度数为( ). A. 52∘ B. 56∘ C. 66∘ D. 76∘","options":[{"label":"A","text":"52∘"},{"label":"B","text":"56∘"},{"label":"C","text":"66∘"},{"label":"D","text":"76∘"}],"answer":"","solution":"","stem_html":"<div>如图，PE、PG为⊙O的两条切线，E、G为切点，点F为⊙O上一点. 连接OE、OG、EF、FG，若∠EFG = 52°, 则∠P的度数为( ).<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/e1726df2-6a02-4aa1-921c-569fde150361/4f94b12f682e.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 52∘<br>B. 56∘<br>C. 66∘<br>D. 76∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:37:37"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:37:37"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:37:37"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:38:35"}],"detail_url":"/questions/25070","edit_url":"/questions/25070/edit","json_url":"/api/questions/25070","recheck_url":"/api/questions/25070/recheck"},{"id":25067,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，△ABC的内切园⊙O分别与AB, BC, AC相切于点D, E, F, 且AD = 3, BE=2, CF = 4, 则△ ABC的周长为( )\\(\\frac{(A)18}{(B)19}\\frac{(C)20}{(D)21}\\)","options":[],"answer":"","solution":"","stem_html":"<div>如图，△ABC的内切园⊙O分别与AB, BC, AC相切于点D, E, F, 且AD = 3, BE=2, CF = 4, 则△ ABC的周长为( )\\(\\frac{(A)18}{(B)19}\\frac{(C)20}{(D)21}\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/169781e5-4d0b-43c1-9b77-075baa6a9454/097640fbf63d.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:35:27"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:35:27"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:35:27"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:35:57"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:36:12"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:36:12"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:36:12"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:36:24"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T06:36:24"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:40:14"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:40:14"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:41:13"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:41:13"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T06:41:13"}],"detail_url":"/questions/25067","edit_url":"/questions/25067/edit","json_url":"/api/questions/25067","recheck_url":"/api/questions/25067/recheck"},{"id":25063,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.725,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图，O是 ABC的内切圆,BOC =117, 则 的度数为( ) A A ．54 55． B C ．56 ．60 D","options":[],"answer":"","solution":"因为BOC = ，\\(\\frac{117}{OCB}\\)OBC + = 180−BOC = 63 ,\\(\\frac{O}{OBOC}\\)ABC的内切圆，  是 , ABC,ACB,\\(\\frac{平分}{2}\\) = , = 2,\\(\\frac{ABC}{ABC} \\frac{OBC}{ACB} \\frac{ACB}{OBC} \\frac{OCB}{OCB}\\) + = 2 + 2 = 2(OBC +) =126,\\(\\frac{OCB}{ABC}\\) =180 − ( +ACB) A =180− 126 = 54 .","stem_html":"<div>如图，O是 ABC的内切圆,BOC =117, 则 的度数为( ) A A ．54 55． B C ．56 ．60 D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/484feaf4-3344-4f61-a2c6-1b183b252ec9/7d9052e83366.png\" style=\"width:151.1px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"因为BOC = ，\\(\\frac{117}{OCB}\\)OBC + = 180−BOC = 63 ,\\(\\frac{O}{OBOC}\\)ABC的内切圆，  是 , ABC,ACB,\\(\\frac{平分}{2}\\) = , = 2,\\(\\frac{ABC}{ABC} \\frac{OBC}{ACB} \\frac{ACB}{OBC} \\frac{OCB}{OCB}\\) + = 2 + 2 = 2(OBC +) =126,\\(\\frac{OCB}{ABC}\\) =180 − ( +ACB) A =180− 126 = 54 .","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:37:57"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:37:57"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:37:57"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T06:38:43"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T06:39:28"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:39:28"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:39:28"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:40:33"},{"type":"QUALITY_GATE","status":"FAIL","score":0.725,"created_at":"2026-09-26T06:40:33"}],"detail_url":"/questions/25063","edit_url":"/questions/25063/edit","json_url":"/api/questions/25063","recheck_url":"/api/questions/25063/recheck"},{"id":25069,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，点\\(O\\)为\\(\\triangle ABC\\)的内心. 若\\(\\angle BOC = 125^{\\circ}\\)，则\\(\\angle A =\\)____．","options":[],"answer":"50^\\(\\circ\\)","solution":"因为点O是\\triangle ABC的内心，所以BO、CO分别是\\(\\angle\\)ABC和\\(\\angle\\)ACB的角平分线。因此，\\(\\angle\\)OBC =\\(\\frac{1}{2}\\angle\\)ABC，\\(\\angle\\)OCB =\\(\\frac{1}{2}\\angle\\)ACB。在\\triangle BOC中，根据三角形内角和定理，有\\(\\angle\\)OBC +\\(\\angle\\)OCB +\\(\\angle\\)BOC = 180^\\(\\circ\\)。已知\\(\\angle\\)BOC = 125^\\(\\circ\\)，所以\\(\\angle\\)OBC +\\(\\angle\\)OCB = 180^\\(\\circ - 125^\\circ = 55^\\circ\\)。从而，\\(\\angle\\)ABC +\\(\\angle\\)ACB = 2(\\(\\angle\\)OBC +\\(\\angle\\)OCB) =\\(2 \\times 55^\\circ = 110^\\circ\\)。最后，在\\triangle ABC中，\\(\\angle\\)A = 180^\\(\\circ - (\\angle ABC + \\angle ACB) = 180^\\circ - 110^\\circ = 70^\\circ\\)。","stem_html":"<div>如图，点\\(O\\)为\\(\\triangle ABC\\)的内心. 若\\(\\angle BOC = 125^{\\circ}\\)，则\\(\\angle A =\\)____．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/7eeeaf5a-0e7c-41f6-b6e3-592ea53353eb/bb351dac0224.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"50^\\(\\circ\\)","solution_html":"因为点O是\\triangle ABC的内心，所以BO、CO分别是\\(\\angle\\)ABC和\\(\\angle\\)ACB的角平分线。因此，\\(\\angle\\)OBC =\\(\\frac{1}{2}\\angle\\)ABC，\\(\\angle\\)OCB =\\(\\frac{1}{2}\\angle\\)ACB。在\\triangle BOC中，根据三角形内角和定理，有\\(\\angle\\)OBC +\\(\\angle\\)OCB +\\(\\angle\\)BOC = 180^\\(\\circ\\)。已知\\(\\angle\\)BOC = 125^\\(\\circ\\)，所以\\(\\angle\\)OBC +\\(\\angle\\)OCB = 180^\\(\\circ - 125^\\circ = 55^\\circ\\)。从而，\\(\\angle\\)ABC +\\(\\angle\\)ACB = 2(\\(\\angle\\)OBC +\\(\\angle\\)OCB) =\\(2 \\times 55^\\circ = 110^\\circ\\)。最后，在\\triangle ABC中，\\(\\angle\\)A = 180^\\(\\circ - (\\angle ABC + \\angle ACB) = 180^\\circ - 110^\\circ = 70^\\circ\\)。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:35:15"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:35:15"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:35:16"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:35:43"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:36:37"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:36:37"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:36:37"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:36:51"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T06:36:51"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T06:38:38"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T06:38:38"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T06:39:36"},{"type":"SYMBOLIC","status":"PASS","score":0.95,"created_at":"2026-09-26T06:39:36"},{"type":"AUTO_REPAIR_ATTEMPT","status":"PASS","score":1.0,"created_at":"2026-09-26T06:39:36"},{"type":"AUTO_REPAIR","status":"PASS","score":1.0,"created_at":"2026-09-26T06:39:36"},{"type":"VISION","status":"FAIL","score":1.0,"created_at":"2026-09-26T06:40:10"}],"detail_url":"/questions/25069","edit_url":"/questions/25069/edit","json_url":"/api/questions/25069","recheck_url":"/api/questions/25069/recheck"},{"id":25066,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[3,4],"stem":"1.如图，PA与⊙O相切于点A，PB与⊙O相切于点B，M为AB上一点，过点M与⊙O相切的直线分别交PA，PB于点E，F.若\\(\\Delta{}PEF\\)的周长为12，则PA的长为( )\\(\\frac{(A)5}{(B)6}\\) C. 7 D. 8","options":[{"label":"C","text":"7"},{"label":"D","text":"8"}],"answer":"","solution":"","stem_html":"<div>1.如图，PA与⊙O相切于点A，PB与⊙O相切于点B，M为AB上一点，过点M与⊙O相切的直线分别交PA，PB于点E，F.若\\(\\Delta{}PEF\\)的周长为12，则PA的长为( )\\(\\frac{(A)5}{(B)6}\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c38aaf66-25ad-43d6-8ab7-eb9a15d823e7/61b0ea6f51e2.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>C. 7<br>D. 8</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:35:29"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:35:29"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:35:29"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T06:36:12"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T06:36:29"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:36:29"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:36:29"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:36:51"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T06:36:51"}],"detail_url":"/questions/25066","edit_url":"/questions/25066/edit","json_url":"/api/questions/25066","recheck_url":"/api/questions/25066/recheck"},{"id":25060,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"内心到三角形三个顶点的连线分别平分","options":[],"answer":"对应的内角","solution":"依据《核心知识点》第3条：内心到三角形三个顶点的连线分别平分对应的内角。","stem_html":"<div>内心到三角形三个顶点的连线分别平分</div>","answer_html":"对应的内角","solution_html":"依据《核心知识点》第3条：内心到三角形三个顶点的连线分别平分对应的内角。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:33:21"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:33:21"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:33:21"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:33:35"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:33:35"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T06:34:13"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:34:13"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:34:34"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:34:34"}],"detail_url":"/questions/25060","edit_url":"/questions/25060/edit","json_url":"/api/questions/25060","recheck_url":"/api/questions/25060/recheck"},{"id":25050,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"三角形内切圆的圆心（内心）是","options":[],"answer":"三角形三个角平分线的交点","solution":"依据：三角形内切圆的圆心（内心）是三角形三个角平分线的交点。内心到三角形三边的距离相等，且分别位于三个内角的平分线上。","stem_html":"<div>三角形内切圆的圆心（内心）是</div>","answer_html":"三角形三个角平分线的交点","solution_html":"依据：三角形内切圆的圆心（内心）是三角形三个角平分线的交点。内心到三角形三边的距离相等，且分别位于三个内角的平分线上。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:31:14"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:31:14"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:31:14"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:31:26"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:31:26"},{"type":"VISION","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:32:11"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:32:11"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T06:32:24"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T06:32:24"}],"detail_url":"/questions/25050","edit_url":"/questions/25050/edit","json_url":"/api/questions/25050","recheck_url":"/api/questions/25050/recheck"},{"id":25045,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"内心到三角形三个顶点的连线分别平分","options":[],"answer":"对应的内角","solution":"依据《核心知识点》第3条：内心到三角形三个顶点的连线分别平分对应的内角。","stem_html":"<div>内心到三角形三个顶点的连线分别平分</div>","answer_html":"对应的内角","solution_html":"依据《核心知识点》第3条：内心到三角形三个顶点的连线分别平分对应的内角。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:30:15"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:30:15"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:30:15"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T06:30:33"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:30:42"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:30:42"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:30:42"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:30:47"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:30:47"}],"detail_url":"/questions/25045","edit_url":"/questions/25045/edit","json_url":"/api/questions/25045","recheck_url":"/api/questions/25045/recheck"},{"id":25041,"job_id":3,"qa_status":"QUARANTINED","question_type":"knowledge","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":1.0,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1405.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"内心到三角形三个顶点的连线分别平分对应的","options":[],"answer":"","solution":"","stem_html":"<div>内心到三角形三个顶点的连线分别平分对应的</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-09-26T06:30:08"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:30:08"},{"type":"VISION","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:30:30"},{"type":"QUALITY_GATE","status":"FAIL","score":1.0,"created_at":"2026-09-26T06:30:30"}],"detail_url":"/questions/25041","edit_url":"/questions/25041/edit","json_url":"/api/questions/25041","recheck_url":"/api/questions/25041/recheck"},{"id":25038,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1400.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，△ABC的周长为22cm, AB = 6cm,⊙O是它的内切园, 直线DE是位于⊙ O右侧的任意一条切线, 若沿着直线DE剪下△CDE, 则剪下的△CDE的周长为( )\\(\\frac{(A)16cm}{(B)12cm}\\) C. 10cm D. 随直线DE的变化而变化","options":[{"label":"C","text":"10cm"},{"label":"D","text":"随直线DE的变化而变化"}],"answer":"","solution":"","stem_html":"<div>如图，△ABC的周长为22cm, AB = 6cm,⊙O是它的内切园, 直线DE是位于⊙ O右侧的任意一条切线, 若沿着直线DE剪下△CDE, 则剪下的△CDE的周长为( )\\(\\frac{(A)16cm}{(B)12cm}\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/f2491b24-2b5a-4aa2-a489-c8a56bc0846b/ce2d1ff4814b.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>C. 10cm<br>D. 随直线DE的变化而变化</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:24:18"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:24:18"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:24:18"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:24:46"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:25:43"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:25:43"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:25:43"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T06:25:51"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T06:25:51"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T06:29:47"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T06:29:47"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:29:47"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-09-26T06:29:47"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T06:29:47"}],"detail_url":"/questions/25038","edit_url":"/questions/25038/edit","json_url":"/api/questions/25038","recheck_url":"/api/questions/25038/recheck"},{"id":25030,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1400.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图四边形,ABCD与 O分别相切于点 E, F,G, H,, ABCD的周长为44,\\(\\frac{其中四边形}{长度为}\\)AD =12,则BC ____．","options":[],"answer":"","solution":" 与 分别相切于点,,,，\\(\\frac{四边形}{DE}\\frac{ABCD}{DHAE} \\frac{O}{AFBF} \\frac{EFGH}{CH}\\) =, =, =, =,\\(\\frac{BGCG}{AF}\\) =12, + + DH + =\\(\\frac{AD}{DE} \\frac{DE}{2}\\frac{AE}{AD} 2(+ AE) = = 24\\) ABCD的周长为，\\(\\frac{44}{CH}\\) + + + = 2(BG + CG)\\(\\frac{BG}{BC} \\frac{CG}{44} \\frac{BF}{24} = 2 =\\)− = 20, BC = 10.","stem_html":"<div>如图四边形,ABCD与 O分别相切于点 E, F,G, H,, ABCD的周长为44,\\(\\frac{其中四边形}{长度为}\\)AD =12,则BC ____．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/83e1409e-40f2-4b50-8319-fc16fd35572c/03eb8bfa1e32.png\" style=\"width:136.0px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":" 与 分别相切于点,,,，\\(\\frac{四边形}{DE}\\frac{ABCD}{DHAE} \\frac{O}{AFBF} \\frac{EFGH}{CH}\\) =, =, =, =,\\(\\frac{BGCG}{AF}\\) =12, + + DH + =\\(\\frac{AD}{DE} \\frac{DE}{2}\\frac{AE}{AD} 2(+ AE) = = 24\\) ABCD的周长为，\\(\\frac{44}{CH}\\) + + + = 2(BG + CG)\\(\\frac{BG}{BC} \\frac{CG}{44} \\frac{BF}{24} = 2 =\\)− = 20, BC = 10.","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:20:34"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:20:34"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:20:34"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T06:21:14"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T06:23:41"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:23:41"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:23:41"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T06:28:29"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T06:28:29"}],"detail_url":"/questions/25030","edit_url":"/questions/25030/edit","json_url":"/api/questions/25030","recheck_url":"/api/questions/25030/recheck"},{"id":25037,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1400.pdf","job_source":"人教版.zip","pages":[4,5],"stem":"如图,\\(PE\\)、\\(PG\\)为\\(\\odot O\\)的两条切线,\\(E\\)、\\(G\\)为切点, 点\\(F\\)为\\(\\odot O\\)上一点. 连接\\(OE\\)、\\(OG\\)、\\(EF\\)、\\(FG\\), 若\\(\\angle EFG = 52^\\circ\\), 则\\(\\angle P\\)的度数为( ). A. 52∘ B. 56∘ C. 66∘ D. 76∘","options":[{"label":"A","text":"52∘"},{"label":"B","text":"56∘"},{"label":"C","text":"66∘"},{"label":"D","text":"76∘"}],"answer":"","solution":"","stem_html":"<div>如图,\\(PE\\)、\\(PG\\)为\\(\\odot O\\)的两条切线,\\(E\\)、\\(G\\)为切点, 点\\(F\\)为\\(\\odot O\\)上一点. 连接\\(OE\\)、\\(OG\\)、\\(EF\\)、\\(FG\\), 若\\(\\angle EFG = 52^\\circ\\), 则\\(\\angle P\\)的度数为( ).<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/ad671cb8-5da5-4340-bf5f-ce5957022bca/1cb3a56722e4.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 52∘<br>B. 56∘<br>C. 66∘<br>D. 76∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:22:56"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:22:56"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:22:56"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:23:36"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T06:26:05"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:26:05"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:26:05"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:26:21"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T06:26:21"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T06:27:19"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:27:19"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:27:36"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-09-26T06:27:36"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:27:36"}],"detail_url":"/questions/25037","edit_url":"/questions/25037/edit","json_url":"/api/questions/25037","recheck_url":"/api/questions/25037/recheck"},{"id":25031,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.762,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1400.pdf","job_source":"人教版.zip","pages":[2,3],"stem":"【小试1】 如图, PA, PB 是 ⊙O 的切线, A, B 为切点,点 C 是优弧 AB 上的一点( 不与A, B重合), 连接AC, BC, 若∠P =\\(\\alpha\\)则∠ACB的度数为( ) A. 90^\\(\\circ+\\frac{1}{2}\\alpha\\) B. 90^\\(\\circ-\\frac{1}{2}\\alpha\\) C. 180∘−\\(\\alpha _{2}\\alpha\\) D. 180∘− 1","options":[{"label":"A","text":"90^ \\circ+\\frac{1}{2}\\alpha"},{"label":"B","text":"90^ \\circ-\\frac{1}{2}\\alpha"},{"label":"C","text":"180∘− \\alpha _{2}\\alpha"},{"label":"D","text":"180∘− 1"}],"answer":"B","solution":"如图, 连接OA, OB, ∵PA, PB是⊙O的切线，∴∠OAP = ∠OBP = 90∘, 又因为∠P =\\(\\alpha\\)，∴∠AOB = 360∘−∠OAP −∠OBP −∠P = 180∘−\\(\\alpha\\)由圆周角定理可知, ∠C = 1 1\\(1 _{2}\\)∠AOB = _{2}(180∘−\\(\\alpha\\)) = 90∘− _{2}\\(\\alpha\\)故选: B． 2.16 设BF = x, 则CF = 6 −x，∵OO是△ABC的内切圆, D, E, F为切点，∴AE = AD=2, BD = BF = x, CE = CF = 6 −x, ∴△ABC的周长= AB + BC + AC = 2(AD+BF + CF) =\\(2 \\times (2 + x + 6 −x) = 16．\\)","stem_html":"<div>【小试1】 如图, PA, PB 是 ⊙O 的切线, A, B 为切点,点 C 是优弧 AB 上的一点( 不与A, B重合), 连接AC, BC, 若∠P =\\(\\alpha\\)则∠ACB的度数为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/d467d004-25ea-4ed4-bc50-d9992642acd7/bda75d821464.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 90^\\(\\circ+\\frac{1}{2}\\alpha\\)<br>B. 90^\\(\\circ-\\frac{1}{2}\\alpha\\)<br>C. 180∘−\\(\\alpha _{2}\\alpha\\)<br>D. 180∘− 1</div>","answer_html":"B","solution_html":"如图, 连接OA, OB, ∵PA, PB是⊙O的切线，∴∠OAP = ∠OBP = 90∘, 又因为∠P =\\(\\alpha\\)，∴∠AOB = 360∘−∠OAP −∠OBP −∠P = 180∘−\\(\\alpha\\)由圆周角定理可知, ∠C = 1 1\\(1 _{2}\\)∠AOB = _{2}(180∘−\\(\\alpha\\)) = 90∘− _{2}\\(\\alpha\\)故选: B． 2.16 设BF = x, 则CF = 6 −x，∵OO是△ABC的内切圆, D, E, F为切点，∴AE = AD=2, BD = BF = x, CE = CF = 6 −x, ∴△ABC的周长= AB + BC + AC = 2(AD+BF + CF) =\\(2 \\times (2 + x + 6 −x) = 16．\\)","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:20:10"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:20:10"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:20:10"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T06:20:42"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:23:31"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:23:31"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:23:31"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T06:24:32"},{"type":"QUALITY_GATE","status":"FAIL","score":0.762,"created_at":"2026-09-26T06:24:32"}],"detail_url":"/questions/25031","edit_url":"/questions/25031/edit","json_url":"/api/questions/25031","recheck_url":"/api/questions/25031/recheck"},{"id":25034,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.922,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1400.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，PA、PB分别与⊙O相切于A、B两点. 若∠C = 70°, 则∠P的度数为( ) A. 70∘ B. 55∘ C. 50∘ D. 40∘","options":[{"label":"A","text":"70∘"},{"label":"B","text":"55∘"},{"label":"C","text":"50∘"},{"label":"D","text":"40∘"}],"answer":"","solution":"","stem_html":"<div>如图，PA、PB分别与⊙O相切于A、B两点. 若∠C = 70°, 则∠P的度数为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/d3c50896-6347-4346-bff1-3254dfc1aca1/ba053e793fc1.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 70∘<br>B. 55∘<br>C. 50∘<br>D. 40∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:18:41"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:18:41"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:18:41"},{"type":"SOLVER","status":"PASS","score":0.99,"created_at":"2026-09-26T06:19:05"},{"type":"CRITIC","status":"PASS","score":0.99,"created_at":"2026-09-26T06:19:05"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:19:22"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:19:22"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T06:19:50"},{"type":"QUALITY_GATE","status":"FAIL","score":0.922,"created_at":"2026-09-26T06:19:50"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T06:21:55"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T06:21:55"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:22:27"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:22:27"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:22:27"}],"detail_url":"/questions/25034","edit_url":"/questions/25034/edit","json_url":"/api/questions/25034","recheck_url":"/api/questions/25034/recheck"},{"id":25000,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案140.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"【小试1】 若关于 x 的一元二次方程的根为 x = 1±\\(\\sqrt{−1}\\)2−\\(4\\times 3\\times (−5)\\)，则这个方程是\\(2\\times 3 ( )\\). A. \\(3x^{2}\\)+ x −5 = 0 B. \\(3x^{2}\\)−x −5 = 0 C. \\(x^{2}\\)−3x −5 = 0 D. \\(x^{2}\\)+ 3x −5 = 0","options":[{"label":"A","text":"3x^{2} + x −5 = 0"},{"label":"B","text":"3x^{2} −x −5 = 0"},{"label":"C","text":"x^{2} −3x −5 = 0"},{"label":"D","text":"x^{2} + 3x −5 = 0"}],"answer":"B","solution":"由题意可得：x = −b±√b2−4ac = 1±\\(\\sqrt{−1}\\)2−\\(4\\times 3\\times (−5)\\)∴−b = 1,2a = 6，解得b = −1, a = 3，∵\\(b^{2}\\)−4ac = 2a\\(2\\times 3 (−1)^{2}−4 \\times 3 \\times (−5)\\)∴c = −5,所以原方程为\\(3x^{2}\\)−x −5 = 0，故选：B．","stem_html":"<div>【小试1】 若关于 x 的一元二次方程的根为 x = 1±\\(\\sqrt{−1}\\)2−\\(4\\times 3\\times (−5)\\)，则这个方程是\\(2\\times 3 ( )\\).<br>A. \\(3x^{2}\\)+ x −5 = 0<br>B. \\(3x^{2}\\)−x −5 = 0<br>C. \\(x^{2}\\)−3x −5 = 0<br>D. \\(x^{2}\\)+ 3x −5 = 0</div>","answer_html":"B","solution_html":"由题意可得：x = −b±√b2−4ac = 1±\\(\\sqrt{−1}\\)2−\\(4\\times 3\\times (−5)\\)∴−b = 1,2a = 6，解得b = −1, a = 3，∵\\(b^{2}\\)−4ac = 2a\\(2\\times 3 (−1)^{2}−4 \\times 3 \\times (−5)\\)∴c = −5,所以原方程为\\(3x^{2}\\)−x −5 = 0，故选：B．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:06:55"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:06:55"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:06:55"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T06:07:21"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:07:41"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:07:41"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:07:41"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:10:35"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T06:10:35"}],"detail_url":"/questions/25000","edit_url":"/questions/25000/edit","json_url":"/api/questions/25000","recheck_url":"/api/questions/25000/recheck"},{"id":25002,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案140.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"−9±\\(\\sqrt{9^{2}}\\)−\\(4\\times 3\\times 1 1\\).用公式法解关于 x 的一元二次方程，得 x =，则该一元二次方程是( ).\\(2\\times 3\\) A. −\\(3x^{2}\\)−9x + 1 = 0 B. \\(3x^{2}\\)−9x + 1 = 0 C. \\(3x^{2}\\)+ 9x + 1 = 0 D. \\(3x^{2}\\)+ 9x −1 = 0","options":[{"label":"A","text":"− 3x^{2} −9x + 1 = 0"},{"label":"B","text":"3x^{2} −9x + 1 = 0"},{"label":"C","text":"3x^{2} + 9x + 1 = 0"},{"label":"D","text":"3x^{2} + 9x −1 = 0"}],"answer":"","solution":"","stem_html":"<div>−9±\\(\\sqrt{9^{2}}\\)−\\(4\\times 3\\times 1 1\\).用公式法解关于 x 的一元二次方程，得 x =，则该一元二次方程是( ).\\(2\\times 3\\)<br>A. −\\(3x^{2}\\)−9x + 1 = 0<br>B. \\(3x^{2}\\)−9x + 1 = 0<br>C. \\(3x^{2}\\)+ 9x + 1 = 0<br>D. \\(3x^{2}\\)+ 9x −1 = 0</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:10:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:10:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:10:11"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T06:10:21"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:10:30"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:10:30"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:10:30"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:10:41"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T06:10:41"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:11:54"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:11:54"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:13:08"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:13:08"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T06:13:08"}],"detail_url":"/questions/25002","edit_url":"/questions/25002/edit","json_url":"/api/questions/25002","recheck_url":"/api/questions/25002/recheck"},{"id":25007,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案140.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"用公式法解下列方程： （1）x(x + 3) = -1. （2）(x + 1)(x −1) = 2√2x．","options":[],"answer":"","solution":"","stem_html":"<div>用公式法解下列方程：<br>（1）x(x + 3) = -1.<br>（2）(x + 1)(x −1) = 2√2x．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-09-26T06:02:38"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:02:38"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:02:38"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:02:49"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:05:23"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:05:23"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:05:23"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:05:36"},{"type":"QUALITY_GATE","status":"FAIL","score":0.975,"created_at":"2026-09-26T06:05:36"}],"detail_url":"/questions/25007","edit_url":"/questions/25007/edit","json_url":"/api/questions/25007","recheck_url":"/api/questions/25007/recheck"},{"id":24998,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案140.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"下列一元二次方程中根是, −\\(2 \\sqrt{2^{2}−−43(1)}\\)x = 的方程是( ) 23\\(Ax^{2}\\)． + −=\\(\\frac{3}{Bx^{2}} \\frac{2}{2}\\frac{x}{x} \\frac{1}{1} \\frac{0}{0}\\)． − −=\\(\\frac{3}{Cx^{2}}\\)．3 + 4 −=1\\(0 \\frac{x}{2}\\)．−\\(x^{2}\\)− x + 3 = 0 D","options":[],"answer":"","solution":"−b 一元二次方程求根公式为x =\\(\\frac{\\sqrt{b^{2}−4ac}}{2}\\)a 对比题目中的公式: 2a = 2 3,a = 3,−= −b2,b = 2, 根号内常数项为 −1,c = −1 因此方程为\\(3x^{2}\\)+ 2x −=1 0. A 故答案: (1)证明计算判别式: : = [−(m + 4)]2 −  m + 3) frac41(3m = + + − − \\(fracm^2m^2\\) frac84fracmm frac164 frac12m frac122)^2 = − + = (−,  任何实数的平方都大于等于即0,(m − 2)^{2}  0,  0. 因此不论取何值方程总有两个实数根,m,. (2)求解定值根 : 方法一因式分解法:\\(x^{2}\\)− (m + 4) + 3 + 3 = (x − 3)(x − (m +1)) =\\(0 \\frac{x}{x_{2}} \\frac{m}{m} = 3, = + \\frac{解得}{其中}\\frac{x_{1}}{x} 1\\). = 3与无关是定值根m,. 方法二代入:特殊值法 令 = 0,方程为\\(x^{2}\\)− 4x + 3 = 0,\\(\\frac{m}{根为}\\)x = 1或3; 令 = 1，方程为\\(x^{2}\\)− 5x + 6 = 0,\\(\\frac{m}{根为}\\)x = 2或3; 两次方程的公共根为x = 3,即为定值根. 故答案这个定值根为: 3.","stem_html":"<div>下列一元二次方程中根是, −\\(2 \\sqrt{2^{2}−−43(1)}\\)x = 的方程是( ) 23\\(Ax^{2}\\)． + −=\\(\\frac{3}{Bx^{2}} \\frac{2}{2}\\frac{x}{x} \\frac{1}{1} \\frac{0}{0}\\)． − −=\\(\\frac{3}{Cx^{2}}\\)．3 + 4 −=1\\(0 \\frac{x}{2}\\)．−\\(x^{2}\\)− x + 3 = 0 D</div>","answer_html":"","solution_html":"−b 一元二次方程求根公式为x =\\(\\frac{\\sqrt{b^{2}−4ac}}{2}\\)a 对比题目中的公式: 2a = 2 3,a = 3,−= −b2,b = 2, 根号内常数项为 −1,c = −1 因此方程为\\(3x^{2}\\)+ 2x −=1 0. A 故答案: (1)证明计算判别式: : = [−(m + 4)]2 −  m + 3)<span class=\"formula-fallback\">frac41(3m = + + − − \\(fracm^2m^2\\) frac84fracmm frac164 frac12m frac122)^2 =</span>− + = (−,  任何实数的平方都大于等于即0,(m − 2)^{2}  0,  0. 因此不论取何值方程总有两个实数根,m,. (2)求解定值根 : 方法一因式分解法:\\(x^{2}\\)− (m + 4) + 3 + 3 = (x − 3)(x − (m +1)) =\\(0 \\frac{x}{x_{2}} \\frac{m}{m} = 3, = + \\frac{解得}{其中}\\frac{x_{1}}{x} 1\\). = 3与无关是定值根m,. 方法二代入:特殊值法 令 = 0,方程为\\(x^{2}\\)− 4x + 3 = 0,\\(\\frac{m}{根为}\\)x = 1或3; 令 = 1，方程为\\(x^{2}\\)− 5x + 6 = 0,\\(\\frac{m}{根为}\\)x = 2或3; 两次方程的公共根为x = 3,即为定值根. 故答案这个定值根为: 3.","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:02:42"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-09-26T06:02:42"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:02:42"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T06:03:30"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:03:45"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:03:45"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:03:45"}],"detail_url":"/questions/24998","edit_url":"/questions/24998/edit","json_url":"/api/questions/24998","recheck_url":"/api/questions/24998/recheck"},{"id":25006,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.937,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案140.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"用公式法解下列方程： （1）\\(4x^{2}\\)−3 = 12x． （2）\\(ax^{2}\\)+ 4x −6 = 0．","options":[],"answer":"","solution":"","stem_html":"<div>用公式法解下列方程：<br>（1）\\(4x^{2}\\)−3 = 12x．<br>（2）\\(ax^{2}\\)+ 4x −6 = 0．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-09-26T06:01:05"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:01:05"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:01:05"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T06:01:32"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T06:01:39"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T06:01:39"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:01:39"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:02:11"},{"type":"QUALITY_GATE","status":"FAIL","score":0.937,"created_at":"2026-09-26T06:02:11"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T06:05:42"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:05:42"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:06:13"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T06:06:13"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:06:13"}],"detail_url":"/questions/25006","edit_url":"/questions/25006/edit","json_url":"/api/questions/25006","recheck_url":"/api/questions/25006/recheck"},{"id":25005,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案140.pdf","job_source":"人教版.zip","pages":[4,5],"stem":"关于x的方程\\(x^{2}\\)−(m + 4)x + 3m + 3 = 0． （1）求证：不论m取何值，方程总有两个实数根； （2）若该方程有两个实数根\\(x_{1}\\),\\(x_{2}\\)，且(\\(x_{1}\\)+ 1)(\\(x_{2}\\)+ 1) = 3，求m的值．","options":[],"answer":"","solution":"","stem_html":"<div>关于x的方程\\(x^{2}\\)−(m + 4)x + 3m + 3 = 0．<br>（1）求证：不论m取何值，方程总有两个实数根；<br>（2）若该方程有两个实数根\\(x_{1}\\),\\(x_{2}\\)，且(\\(x_{1}\\)+ 1)(\\(x_{2}\\)+ 1) = 3，求m的值．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:00:36"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:00:36"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:00:36"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T06:00:55"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T06:02:03"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:02:03"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:02:03"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:02:10"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T06:02:10"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:02:50"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:02:50"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:05:54"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T06:05:54"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:05:54"}],"detail_url":"/questions/25005","edit_url":"/questions/25005/edit","json_url":"/api/questions/25005","recheck_url":"/api/questions/25005/recheck"},{"id":25003,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案140.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"−b±\\(\\sqrt{b^{2}}\\)−4ac 2.在用求根公式 x = 求一元二次方程的根时，佳琪正确地代入了 a, b, c 得到 x = 2a −3±\\(\\sqrt{3^{2}}\\)−\\(4\\times 2\\times (−1)\\)，则她求解的一元二次方程是( ).\\(2\\times 2\\) A. \\(2x^{2}\\)−3x −1 = 0 B. \\(2x^{2}\\)+ 3x −1 = 0 C. \\(2x^{2}\\)+ 3x + 1 = 0 D. \\(2x^{2}\\)−3x + 1 = 0","options":[{"label":"A","text":"2x^{2} −3x −1 = 0"},{"label":"B","text":"2x^{2} + 3x −1 = 0"},{"label":"C","text":"2x^{2} + 3x + 1 = 0"},{"label":"D","text":"2x^{2} −3x + 1 = 0"}],"answer":"","solution":"","stem_html":"<div>−b±\\(\\sqrt{b^{2}}\\)−4ac 2.在用求根公式 x = 求一元二次方程的根时，佳琪正确地代入了 a, b, c 得到 x = 2a −3±\\(\\sqrt{3^{2}}\\)−\\(4\\times 2\\times (−1)\\)，则她求解的一元二次方程是( ).\\(2\\times 2\\)<br>A. \\(2x^{2}\\)−3x −1 = 0<br>B. \\(2x^{2}\\)+ 3x −1 = 0<br>C. \\(2x^{2}\\)+ 3x + 1 = 0<br>D. \\(2x^{2}\\)−3x + 1 = 0</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T06:03:01"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T06:03:01"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T06:03:01"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T06:03:27"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T06:03:52"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T06:03:52"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:03:52"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:04:06"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-09-26T06:04:06"}],"detail_url":"/questions/25003","edit_url":"/questions/25003/edit","json_url":"/api/questions/25003","recheck_url":"/api/questions/25003/recheck"},{"id":25004,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案140.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"关于x的方程\\(3x^{2}\\)+ (m + 3)x + m = 0． （1）求证：不论m取何值，方程总有两个实数根； （2）若方程有两个相等的实数根，请求出m的值并求此时方程的根．","options":[],"answer":"","solution":"","stem_html":"<div>关于x的方程\\(3x^{2}\\)+ (m + 3)x + m = 0．<br>（1）求证：不论m取何值，方程总有两个实数根；<br>（2）若方程有两个相等的实数根，请求出m的值并求此时方程的根．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:59:43"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:59:43"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:59:43"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T06:00:00"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T06:01:19"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:01:19"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T06:01:19"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T06:01:39"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T06:01:39"}],"detail_url":"/questions/25004","edit_url":"/questions/25004/edit","json_url":"/api/questions/25004","recheck_url":"/api/questions/25004/recheck"},{"id":24968,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案135.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"用公式法解下列方程：\\(4x^{2}\\)−3 = 12x；\\(\\frac{(1)}{(2)}2x^{2}−5x + 3 = 0．\\)","options":[],"answer":"2 2","solution":"(1)\\(4x^{2}\\)−3 = 12x，化为一般形式：\\(4x^{2}\\)−12x −3 = 0,\\(\\Delta = (−12)^{2}−4 \\times 4\\times 12\\)± √192 3 ± 2√3 3 + 2√3 3 −2√3 (−3) = 192 &gt; 0，则x = =，所以\\(x_{1}\\)=,\\(x_{2}\\)= ．\\(2 \\times 4 2 2 2\\)(2)\\(2x^{2}\\)−5x + 3 = 0,\\(\\Delta = (−5)^{2}−4 \\times 2 \\times 3 = 1\\)&gt; 0，则x = 5 ± √1，所以\\(x_{1}\\)=\\(\\frac{3}{2}x_{2}\\)= 1．\\(2 \\times 2 3 + 2√3 3\\)−2√3 (1)\\(x_{1}\\)=,\\(x_{2}\\)= ．(2)①当a= 0时，解为x=\\(\\frac{3}{2}\\)；②当","stem_html":"<div>用公式法解下列方程：\\(4x^{2}\\)−3 = 12x；\\(\\frac{(1)}{(2)}2x^{2}−5x + 3 = 0．\\)</div>","answer_html":"2 2","solution_html":"(1)\\(4x^{2}\\)−3 = 12x，化为一般形式：\\(4x^{2}\\)−12x −3 = 0,\\(\\Delta = (−12)^{2}−4 \\times 4\\times 12\\)± √192 3 ± 2√3 3 + 2√3 3 −2√3 (−3) = 192 &gt; 0，则x = =，所以\\(x_{1}\\)=,\\(x_{2}\\)= ．\\(2 \\times 4 2 2 2\\)(2)\\(2x^{2}\\)−5x + 3 = 0,\\(\\Delta = (−5)^{2}−4 \\times 2 \\times 3 = 1\\)&gt; 0，则x = 5 ± √1，所以\\(x_{1}\\)=\\(\\frac{3}{2}x_{2}\\)= 1．\\(2 \\times 2 3 + 2√3 3\\)−2√3 (1)\\(x_{1}\\)=,\\(x_{2}\\)= ．(2)①当a= 0时，解为x=\\(\\frac{3}{2}\\)；②当","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-09-26T05:40:41"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:40:41"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:40:41"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:41:25"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T05:41:36"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T05:41:36"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T05:41:36"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T05:45:07"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T05:45:07"}],"detail_url":"/questions/24968","edit_url":"/questions/24968/edit","json_url":"/api/questions/24968","recheck_url":"/api/questions/24968/recheck"},{"id":24969,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.912,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案135.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"用公式法解下列方程：\\(4x^{2}\\)−3 = 12x．\\(\\frac{(1)}{(2)}ax^{2}+ 4x\\)−6 = 0．","options":[],"answer":"2 2","solution":"−2 + √4 + 6a −2 −√4 + 6a a≥−\\(\\frac{2}{3}\\)且a ≠0时，\\(x_{1}\\)= a,\\(x_{2}\\)= a ;③当a&lt; −\\(\\frac{2}{3}\\)时，原方程无实数解． (1)方程整理为\\(4x^{2}\\)−12x −3 = 0. ∵a = 4, b = −12, c = −3, ∴\\(b^{2}\\)−4ac= 144 −\\(4 \\times 4 \\times (−3) = 192\\)&gt; 0∴ x= 12 ± √192 = 3 ± 2√3 ∴\\(x_{1}\\)= 3 + 2√3,且\\(x_{2}\\)=3 −2√3 8 2 2 2 (2)①当a= 0时，原方程为4x−6 = 0，解得x=\\(\\frac{3}{2}\\)；②当a≠0，且\\(\\Delta=\\)−4 ± √16 + 24a\\(4^{2}\\)−4a ⋅(−6) = 16 + 24a ≥0, 即a ≥−\\(\\frac{2}{3}\\)且a≠0时,x= = 2a −2 ± √4 + 6a −2 + √4 + 6a −2 −√4 + 6a a, ∴\\(x_{1}\\)= a,\\(x_{2}\\)= a ③当a≠0，且\\(4^{2}\\)−4a ⋅(−6) = 16 + 24a &lt; 0，即a &lt; −\\(\\frac{2}{3}\\)时，原方程无实数解． −3 + √5 −3 −√5","stem_html":"<div>用公式法解下列方程：\\(4x^{2}\\)−3 = 12x．\\(\\frac{(1)}{(2)}ax^{2}+ 4x\\)−6 = 0．</div>","answer_html":"2 2","solution_html":"−2 + √4 + 6a −2 −√4 + 6a a≥−\\(\\frac{2}{3}\\)且a ≠0时，\\(x_{1}\\)= a,\\(x_{2}\\)= a ;③当a&lt; −\\(\\frac{2}{3}\\)时，原方程无实数解． (1)方程整理为\\(4x^{2}\\)−12x −3 = 0. ∵a = 4, b = −12, c = −3, ∴\\(b^{2}\\)−4ac= 144 −\\(4 \\times 4 \\times (−3) = 192\\)&gt; 0∴ x= 12 ± √192 = 3 ± 2√3 ∴\\(x_{1}\\)= 3 + 2√3,且\\(x_{2}\\)=3 −2√3 8 2 2 2 (2)①当a= 0时，原方程为4x−6 = 0，解得x=\\(\\frac{3}{2}\\)；②当a≠0，且\\(\\Delta=\\)−4 ± √16 + 24a\\(4^{2}\\)−4a ⋅(−6) = 16 + 24a ≥0, 即a ≥−\\(\\frac{2}{3}\\)且a≠0时,x= = 2a −2 ± √4 + 6a −2 + √4 + 6a −2 −√4 + 6a a, ∴\\(x_{1}\\)= a,\\(x_{2}\\)= a ③当a≠0，且\\(4^{2}\\)−4a ⋅(−6) = 16 + 24a &lt; 0，即a &lt; −\\(\\frac{2}{3}\\)时，原方程无实数解． −3 + √5 −3 −√5","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-09-26T05:41:01"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:41:01"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:41:01"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T05:41:27"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T05:42:10"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T05:42:10"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T05:42:10"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T05:43:58"},{"type":"QUALITY_GATE","status":"FAIL","score":0.912,"created_at":"2026-09-26T05:43:58"}],"detail_url":"/questions/24969","edit_url":"/questions/24969/edit","json_url":"/api/questions/24969","recheck_url":"/api/questions/24969/recheck"},{"id":24961,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.775,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案135.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"若关于x的一元二次方程\\(x^{2}\\)+ √ax + 1 = 0有两个相等的实数根，则实数a的值是( ). A. \\(\\frac{1}{4}\\) B. −1\\(4 \\frac{(C)4}{(D)-4}\\)","options":[{"label":"A","text":"\\frac{1}{4}"},{"label":"B","text":"−1 4 \\frac{(C)4}{(D)-4}"}],"answer":"C","solution":"根据题意得\\(\\Delta = (\\sqrt{a})^{2}-4 \\times 1 \\times 1 = 0\\)，解得a = 4．故选：C．","stem_html":"<div>若关于x的一元二次方程\\(x^{2}\\)+ √ax + 1 = 0有两个相等的实数根，则实数a的值是(    ).<br>A. \\(\\frac{1}{4}\\)<br>B. −1\\(4 \\frac{(C)4}{(D)-4}\\)</div>","answer_html":"C","solution_html":"根据题意得\\(\\Delta = (\\sqrt{a})^{2}-4 \\times 1 \\times 1 = 0\\)，解得a = 4．故选：C．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:36:03"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:36:03"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:36:03"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T05:36:20"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T05:36:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T05:36:38"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T05:36:38"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T05:36:53"},{"type":"QUALITY_GATE","status":"FAIL","score":0.775,"created_at":"2026-09-26T05:36:53"}],"detail_url":"/questions/24961","edit_url":"/questions/24961/edit","json_url":"/api/questions/24961","recheck_url":"/api/questions/24961/recheck"},{"id":24957,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图（1），中国古代的马车已经涉及很复杂的机械设计，包含大量零 部件和工艺，所彰显的智慧让人叹服．如图（2）是马车的侧面示意 图，AB为车轮 ⊙ O的直径，过圆心O的车架AC一端点C着地时，地面 CD与车轮⊙O相切于点D，连接AD, BD． （1）求证：∠A= ∠BDC； （2）若\\(\\angle A = 40^\\circ\\),\\(\\angle C\\)的度数是____； （3）若\\(\\frac{BD}{AD} = \\frac{5}{6},BC = 2.5\\)米，求车轮的半径长．","options":[],"answer":"(1)见解析(2)10∘(3)0.55m","solution":"(1)证明：∵CD与⊙O相切∴OD ⊥CD ∴∠ODB + ∠BDC= 90∘∵AB为 ⊙O的直径，∴∠ADB = 90∘, ∴∠A + ∠OBD = 90∘, ∵OB = OD，∴∠ODB= ∠OBD, ∴∠A = ∠BDC； (2)∵OA = OD, ∠A = 40∘∴∠A = ∠ODA = 40∘∵CD与⊙O相切∴ ∠ODC= 90∘∴∠ADC= ∠ODA + ∠ODC= 40∘+ 90∘= 130∘∴ ∠C= 180∘−∠A −∠ADC= 180∘−40∘−130∘= 10∘； (3)由(1)得 : ∠A= ∠BDC ∵ ∠C = ∠C ∴△ CBD∼△ CBA(AA),∴\\(\\frac{BC}{CD} = \\frac{CD}{CA} = \\frac{BD}{AD},∵\\)BC = 2.5,\\(\\frac{BD}{AD} = \\frac{5}{6},∴ \\frac{2.5}{CD} = \\frac{CD}{2.5 + AB} = \\frac{5}{6},∴\\)CD= 3,AB= 1.1∴ AO=BO=\\(\\frac{1}{2}\\)AB= 0.55.","stem_html":"<div>如图（1），中国古代的马车已经涉及很复杂的机械设计，包含大量零 部件和工艺，所彰显的智慧让人叹服．如图（2）是马车的侧面示意 图，AB为车轮 ⊙ O的直径，过圆心O的车架AC一端点C着地时，地面 CD与车轮⊙O相切于点D，连接AD, BD．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/da0de3d9-528e-4626-9e39-b7b67c3ad16d/d8dc744785b9.png\" style=\"width:257.2px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）求证：∠A= ∠BDC；<br>（2）若\\(\\angle A = 40^\\circ\\),\\(\\angle C\\)的度数是____；<br>（3）若\\(\\frac{BD}{AD} = \\frac{5}{6},BC = 2.5\\)米，求车轮的半径长．</div>","answer_html":"(1)见解析(2)10∘(3)0.55m","solution_html":"(1)证明：∵CD与⊙O相切∴OD ⊥CD ∴∠ODB + ∠BDC= 90∘∵AB为 ⊙O的直径，∴∠ADB = 90∘, ∴∠A + ∠OBD = 90∘, ∵OB = OD，∴∠ODB= ∠OBD, ∴∠A = ∠BDC； (2)∵OA = OD, ∠A = 40∘∴∠A = ∠ODA = 40∘∵CD与⊙O相切∴ ∠ODC= 90∘∴∠ADC= ∠ODA + ∠ODC= 40∘+ 90∘= 130∘∴ ∠C= 180∘−∠A −∠ADC= 180∘−40∘−130∘= 10∘； (3)由(1)得 :  ∠A= ∠BDC ∵ ∠C = ∠C ∴△ CBD∼△ CBA(AA),∴\\(\\frac{BC}{CD} = \\frac{CD}{CA} = \\frac{BD}{AD},∵\\)BC = 2.5,\\(\\frac{BD}{AD} = \\frac{5}{6},∴ \\frac{2.5}{CD} = \\frac{CD}{2.5 + AB} = \\frac{5}{6},∴\\)CD= 3,AB= 1.1∴ AO=BO=\\(\\frac{1}{2}\\)AB= 0.55.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:27:08"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:27:08"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:27:08"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:27:38"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T05:29:35"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T05:29:35"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T05:29:35"},{"type":"COHERENCE","status":"WARN","score":0.6,"created_at":"2026-09-26T05:31:05"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T05:31:05"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T05:33:23"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:33:23"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.5,"created_at":"2026-09-26T05:33:23"}],"detail_url":"/questions/24957","edit_url":"/questions/24957/edit","json_url":"/api/questions/24957","recheck_url":"/api/questions/24957/recheck"},{"id":24956,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"孔明喜欢骑自行车玩，如图1是一辆自行车，图2是后轮及部分车架示意 图：车架斜杆MO交车轮 ⊙ O于点C，延长斜杆MO与 ⊙ O交于另一点 D，与地平线NB交于点A，连接BC，车架横杆OP与BC交于点E．已知 OE//AB，车轮⊙O与地平线BN是相切的，点B是切点． 若∠A = 30∘，求∠C度数；．\\(\\frac{(1)}{(2)}\\)若AD = 1m, AB = 1.3m，①求自行车的半径；②求线段OE的长度．","options":[],"answer":"(1)30°(2)①0.345m②0.265m","solution":"(1)如图：连接OB， ∵ ⊙O与BN是相切于点B， ∴ ∠ABO= 90°∵ ∠A= 30°，∴ ∠AOB= 90° −∠A= 60°∴ ∠C =\\(\\frac{1}{2}\\)∠AOB= 30° (2)①设⊙O的半径为r，则OB = OD = r, OA = r + 1 ∵\\(OA^{2}\\)=\\(OB^{2}\\)+\\(AB^{2}\\)，∴ (r + 1)^{2}=\\(r^{2}\\)+ 1.\\(3^{2}\\)，解得：r = 0.345m ②由题意可得：OC = 0.345,AC =AD+OD+OC = 1 + 0.345 + 0.345 = 1.69∵ OE ∥ AB∴△ COE ∽△ CAB∴\\(\\frac{OE}{AB} = \\frac{OC}{AC}\\)即\\(\\frac{OE}{1.3} = \\frac{0.345}{1.69}\\)解得OE = 0.265m AI智适化学案 学案ID:R10911335064 初三","stem_html":"<div>孔明喜欢骑自行车玩，如图1是一辆自行车，图2是后轮及部分车架示意 图：车架斜杆MO交车轮 ⊙ O于点C，延长斜杆MO与 ⊙ O交于另一点 D，与地平线NB交于点A，连接BC，车架横杆OP与BC交于点E．已知 OE//AB，车轮⊙O与地平线BN是相切的，点B是切点． 若∠A = 30∘，求∠C度数；．\\(\\frac{(1)}{(2)}\\)若AD = 1m, AB = 1.3m，①求自行车的半径；②求线段OE的长度．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/fec98172-ba47-40c8-bb86-a80f0707680f/6f951758816c.png\" style=\"width:257.2px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"(1)30°(2)①0.345m②0.265m","solution_html":"(1)如图：连接OB， ∵ ⊙O与BN是相切于点B， ∴ ∠ABO= 90°∵ ∠A= 30°，∴ ∠AOB= 90° −∠A= 60°∴ ∠C =\\(\\frac{1}{2}\\)∠AOB= 30° (2)①设⊙O的半径为r，则OB = OD = r, OA = r + 1 ∵\\(OA^{2}\\)=\\(OB^{2}\\)+\\(AB^{2}\\)，∴ (r + 1)^{2}=\\(r^{2}\\)+ 1.\\(3^{2}\\)，解得：r = 0.345m ②由题意可得：OC = 0.345,AC =AD+OD+OC = 1 + 0.345 + 0.345 = 1.69∵ OE ∥ AB∴△ COE ∽△ CAB∴\\(\\frac{OE}{AB} = \\frac{OC}{AC}\\)即\\(\\frac{OE}{1.3} = \\frac{0.345}{1.69}\\)解得OE = 0.265m AI智适化学案 学案ID:R10911335064 初三","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:25:58"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:25:58"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:25:58"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:26:28"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T05:30:42"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:30:42"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:30:42"},{"type":"COHERENCE","status":"WARN","score":0.6,"created_at":"2026-09-26T05:32:53"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T05:32:53"}],"detail_url":"/questions/24956","edit_url":"/questions/24956/edit","json_url":"/api/questions/24956","recheck_url":"/api/questions/24956/recheck"},{"id":24958,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[5,6],"stem":"如图，AB为⊙O的直径，C为⊙O上一点，连接AC、BC，点F为CB上一点，且CF=CA，延长BF于点E，使得CE⊥BE，延长EC、BA交于点D．求证：DE是⊙O的切线；","options":[],"answer":"见解析","solution":"证明：如图所示，连接 OC，∵ CF = CA,∴ ∠ABC = ∠EBC ∵ OB=OC∴ ∠OCB= ∠ABC,∴ ∠OCB= ∠EBC,∴ OC ∥ BE ∵ CE ⊥ BE,∴ CE ⊥ OC又 ∵OC是⊙O的半径，∴DE是⊙O的切线","stem_html":"<div>如图，AB为⊙O的直径，C为⊙O上一点，连接AC、BC，点F为CB上一点，且CF=CA，延长BF于点E，使得CE⊥BE，延长EC、BA交于点D．求证：DE是⊙O的切线；<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/f57ad4a6-11e1-4d6f-ae4c-d801b6ba85ad/938e91b53b87.png\" style=\"width:180.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"见解析","solution_html":"证明：如图所示，连接 OC，∵ CF = CA,∴ ∠ABC = ∠EBC ∵ OB=OC∴ ∠OCB= ∠ABC,∴ ∠OCB= ∠EBC,∴ OC ∥ BE ∵ CE ⊥ BE,∴ CE ⊥ OC又 ∵OC是⊙O的半径，∴DE是⊙O的切线","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:24:46"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:24:46"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:24:46"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:25:26"}],"detail_url":"/questions/24958","edit_url":"/questions/24958/edit","json_url":"/api/questions/24958","recheck_url":"/api/questions/24958/recheck"},{"id":24955,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[4,5],"stem":"如图，在Rt △ABC中，∠C= 90°，以AC为直径的⊙O交AB于点D，点Q为 CA延长线上一点，延长QD交BC于点P，连接OD, ∠ADQ=\\(\\frac{1}{2}\\)∠DOQ．求证：PD是 ⊙ O的切线；解答题，第一题8分，第二题10分，第三题10分","options":[],"answer":"见解析","solution":"连接DC∵\\widehat{AD}=\\widehat{AD},∴∠DCA=\\(\\frac{1}{2}∠DOA∵∠ADQ=\\frac{1}{2}∠DOQ∴∠DCA=∠ADQ,∵AC\\)为直径,∴∠ADC=90^{\\(\\circ\\)},∴∠DCA+∠DAC=90^{\\(\\circ\\)}∵∠ADQ+∠DAC=90^{\\(\\circ\\)},∠ADO=∠DAC,∴∠ADQ+∠ADO=90^{\\(\\circ\\)},∴PD是⊙O的切线","stem_html":"<div>如图，在Rt △ABC中，∠C= 90°，以AC为直径的⊙O交AB于点D，点Q为 CA延长线上一点，延长QD交BC于点P，连接OD, ∠ADQ=\\(\\frac{1}{2}\\)∠DOQ．求证：PD是 ⊙ O的切线；解答题，第一题8分，第二题10分，第三题10分<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/efc09351-49d2-4b16-a614-a6bce3b5e58f/7babc1f8b4cc.png\" style=\"width:180.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"见解析","solution_html":"连接DC∵\\widehat{AD}=\\widehat{AD},∴∠DCA=\\(\\frac{1}{2}∠DOA∵∠ADQ=\\frac{1}{2}∠DOQ∴∠DCA=∠ADQ,∵AC\\)为直径,∴∠ADC=90^{\\(\\circ\\)},∴∠DCA+∠DAC=90^{\\(\\circ\\)}∵∠ADQ+∠DAC=90^{\\(\\circ\\)},∠ADO=∠DAC,∴∠ADQ+∠ADO=90^{\\(\\circ\\)},∴PD是⊙O的切线","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:23:04"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:23:04"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:23:04"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:23:29"}],"detail_url":"/questions/24955","edit_url":"/questions/24955/edit","json_url":"/api/questions/24955","recheck_url":"/api/questions/24955/recheck"},{"id":24944,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"如图，已知\\(\\triangle ABC\\)，以\\(BC\\)为直径的\\(\\odot O\\)交\\(AB\\)于点\\(D\\)，与\\(AC\\)相切于点\\(C\\)，\\(E\\)是\\(\\overset{\\frown}{BC}\\)上一点，连接\\(BE\\)，\\(DE\\)，若\\(\\angle A = 50^{\\circ}\\)，则\\(\\angle E\\)的度数是( ) A. 20∘ B. 25∘ C. 40∘ D. 50∘","options":[{"label":"A","text":"20∘"},{"label":"B","text":"25∘"},{"label":"C","text":"40∘"},{"label":"D","text":"50∘"}],"answer":"D","solution":"连接CD，则∠E = ∠BCD， ∵ 以BC为直径的 ⊙ O交AB于点D，与AC相切 于点C，∴∠BCA = 90∘, ∠BDC= 90∘, ∵∠A = 50∘, ∴∠ABC= 90∘−∠A= 40∘, ∴∠DCB = 90∘−∠ABC= 50∘, ∴∠E= ∠BCD = 50∘.","stem_html":"<div>如图，已知\\(\\triangle ABC\\)，以\\(BC\\)为直径的\\(\\odot O\\)交\\(AB\\)于点\\(D\\)，与\\(AC\\)相切于点\\(C\\)，\\(E\\)是\\(\\overset{\\frown}{BC}\\)上一点，连接\\(BE\\)，\\(DE\\)，若\\(\\angle A = 50^{\\circ}\\)，则\\(\\angle E\\)的度数是(     )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/4561aeca-df48-4d6d-bdaa-79aa8533c36d/d78df0beabbb.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 20∘<br>B. 25∘<br>C. 40∘<br>D. 50∘</div>","answer_html":"D","solution_html":"连接CD，则∠E = ∠BCD， ∵ 以BC为直径的 ⊙ O交AB于点D，与AC相切 于点C，∴∠BCA = 90∘, ∠BDC= 90∘, ∵∠A = 50∘, ∴∠ABC= 90∘−∠A= 40∘, ∴∠DCB = 90∘−∠ABC= 50∘, ∴∠E= ∠BCD = 50∘.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:17:43"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-09-26T05:17:43"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:17:43"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T05:18:19"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T05:20:47"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:20:47"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:20:47"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T05:24:17"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T05:24:17"}],"detail_url":"/questions/24944","edit_url":"/questions/24944/edit","json_url":"/api/questions/24944","recheck_url":"/api/questions/24944/recheck"},{"id":24952,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，四边形\\(ABCD\\)是\\odot O的内接四边形，点\\(O\\)在四边形\\)ABCD\\(内部，过点C\\)作\\(\\odot O\\)的切线交\\(AB\\)的延长线于点\\(P\\)，连接\\)OA,OB\\)．若\\(\\angle\\)AOB= 140^{\\(\\circ\\)}, angle BCP= 35^\\(circ，则\\(angle ADC的度数为____ 。","options":[],"answer":"105∘","solution":"连接OC, ∵点C为切点∴OC⊥PC, ∴∠OCP= 90∘, ∵∠BCP= 35∘∴ ∠OCB = 90∘−∠BCP= 55∘, ∵OC= OB, ∴∠OBC= ∠OCB = 55∘∴ ∠BOC= 180∘−∠OCB −∠OBC= 70∘, ∵∠AOB = 140∘, ∴∠AOC= 360∘−∠AOB −∠BOC= 150∘, ∴∠ABC=\\(\\frac{1}{2}\\)∠AOC= 75∘, ∴∠ADC=180∘−∠ABC= 105∘. 85∘.","stem_html":"<div>如图，四边形\\(ABCD\\)是\\odot O的内接四边形，点\\(O\\)在四边形\\)ABCD\\(内部，过点C\\)作\\(\\odot O\\)的切线交\\(AB\\)的延长线于点\\(P\\)，连接\\)OA,OB\\)．若\\(\\angle\\)AOB= 140^{\\(\\circ\\)}, <span class=\"formula-fallback\">angle BCP= 35^\\(circ，则\\(angle ADC的度数为____</span>。<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/e8f53181-167e-4f97-a573-3d10b92a5482/b70b86dac721.png\" style=\"width:180.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"105∘","solution_html":"连接OC, ∵点C为切点∴OC⊥PC, ∴∠OCP= 90∘, ∵∠BCP= 35∘∴ ∠OCB = 90∘−∠BCP= 55∘, ∵OC= OB, ∴∠OBC= ∠OCB = 55∘∴ ∠BOC= 180∘−∠OCB −∠OBC= 70∘, ∵∠AOB = 140∘, ∴∠AOC= 360∘−∠AOB −∠BOC= 150∘, ∴∠ABC=\\(\\frac{1}{2}\\)∠AOC= 75∘, ∴∠ADC=180∘−∠ABC= 105∘. 85∘.","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:20:44"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:20:44"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:20:44"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:21:19"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T05:22:34"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T05:22:34"},{"type":"SYMBOLIC","status":"PASS","score":0.95,"created_at":"2026-09-26T05:22:34"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T05:23:48"},{"type":"QUALITY_GATE","status":"PASS","score":0.95,"created_at":"2026-09-26T05:23:48"}],"detail_url":"/questions/24952","edit_url":"/questions/24952/edit","json_url":"/api/questions/24952","recheck_url":"/api/questions/24952/recheck"},{"id":24951,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，四边形$ABCD 是\\(odot O\\)的内接四边形，\\(AD=AB=BC\\)，直线\\(EC\\)与\\(odot O\\)相切于点\\(C\\)．若已知\\(angle ABC = 100^circ\\)，则\\(angle DCE\\)的度数为____ 。","options":[],"answer":"  ","solution":"连接OA,OB,OC,OD,∵ AD=AB=BC,∴ AD = AB = BC， ∴ ∠AOD= ∠AOB= ∠BOC，设∠AOD= ∠AOB= ∠BOC =\\(\\alpha\\)，在 △ OAB和 180∘−\\(\\alpha\\)△OBC中OA = OB = OC, ∴∠OBA = ∠OBC= ,∴ ∠ABC= 2 ∠OBA + ∠OBC= 180∘−\\(\\alpha\\)∵∠ABC= 100∘, ∴180∘−\\(\\alpha = 100∘\\)，解得\\(\\alpha = 80∘\\)∴∠AOD = ∠AOB = ∠BOC= 80∘∴∠ADO =180∘−∠AOD = 2 180∘−80∘ = 50∘, ∵四边形ABCD内接于⊙O，∴∠ADC= 180∘−∠ABC= 2 180∘−100∘= 80∘, ∴∠ODC= ∠ADC −∠ODA = 80∘−50∘= 30∘，∵OD= OC, ∴∠OCD = ∠ODC= 30∘, ∵直线EC与⊙O相切于点C∴∠OCE= 90∘，∴∠DCE= ∠OCE −∠OCD = 90∘−30∘= 60∘． 105∘","stem_html":"<div>如图，四边形$ABCD<span class=\"formula-fallback\">是\\(odot O\\)的内接四边形，\\(AD=AB=BC\\)，直线\\(EC\\)与\\(odot O\\)相切于点\\(C\\)．若已知\\(angle ABC = 100^circ\\)，则\\(angle DCE\\)的度数为____</span>。<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/b474035f-b306-4ae2-a4ff-c8c3c7826b57/1f2e71117890.png\" style=\"width:180.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"  ","solution_html":"连接OA,OB,OC,OD,∵ AD=AB=BC,∴ AD = AB = BC， ∴ ∠AOD= ∠AOB= ∠BOC，设∠AOD= ∠AOB= ∠BOC =\\(\\alpha\\)，在 △ OAB和 180∘−\\(\\alpha\\)△OBC中OA = OB = OC, ∴∠OBA = ∠OBC= ,∴ ∠ABC= 2 ∠OBA + ∠OBC= 180∘−\\(\\alpha\\)∵∠ABC= 100∘, ∴180∘−\\(\\alpha = 100∘\\)，解得\\(\\alpha = 80∘\\)∴∠AOD = ∠AOB = ∠BOC= 80∘∴∠ADO =180∘−∠AOD = 2 180∘−80∘ = 50∘, ∵四边形ABCD内接于⊙O，∴∠ADC= 180∘−∠ABC= 2 180∘−100∘= 80∘, ∴∠ODC= ∠ADC −∠ODA = 80∘−50∘= 30∘，∵OD= OC, ∴∠OCD = ∠ODC= 30∘, ∵直线EC与⊙O相切于点C∴∠OCE= 90∘，∴∠DCE= ∠OCE −∠OCD = 90∘−30∘= 60∘． 105∘","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:17:15"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:17:15"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:17:15"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:18:13"}],"detail_url":"/questions/24951","edit_url":"/questions/24951/edit","json_url":"/api/questions/24951","recheck_url":"/api/questions/24951/recheck"},{"id":24950,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，四边形$ABCD 为\\(odot O\\)的内接四边形，\\(AB\\)为\\(odot O\\)的直径，点\\(P\\)在\\(BA\\)的延长线上，\\(PD\\)与\\(odot O\\)相切，切点为\\(D\\)，若\\(angle BCD = 130^circ\\)，则\\(angle P\\)的大小为( ) A. 80∘ B. 40∘ C. 20∘ D. 10∘","options":[{"label":"A","text":"80∘"},{"label":"B","text":"40∘"},{"label":"C","text":"20∘"},{"label":"D","text":"10∘"}],"answer":"D","solution":"连接OD, ∵四边形ABCD为⊙O的内接四边形，∠BCD = 130∘，∴∠OAD= 180∘−∠BCD = 50∘, ∵ OA=OD, ∴∠OAD = ∠ODA = 50∘, ∴∠AOD= 180∘−∠OAD −∠ODA = 80∘, ∵PD与⊙O相切，∴∠ODP= 90∘，∴∠P90∘−∠DOP= 10∘.= 60∘","stem_html":"<div>如图，四边形$ABCD<span class=\"formula-fallback\">为\\(odot O\\)的内接四边形，\\(AB\\)为\\(odot O\\)的直径，点\\(P\\)在\\(BA\\)的延长线上，\\(PD\\)与\\(odot O\\)相切，切点为\\(D\\)，若\\(angle BCD = 130^circ\\)，则\\(angle P\\)的大小为(     )</span><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/63ada9bb-c4e9-4a13-86de-289f8970f119/21658048c78f.png\" style=\"width:180.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 80∘<br>B. 40∘<br>C. 20∘<br>D. 10∘</div>","answer_html":"D","solution_html":"连接OD, ∵四边形ABCD为⊙O的内接四边形，∠BCD = 130∘，∴∠OAD= 180∘−∠BCD = 50∘, ∵ OA=OD, ∴∠OAD = ∠ODA = 50∘, ∴∠AOD= 180∘−∠OAD −∠ODA = 80∘, ∵PD与⊙O相切，∴∠ODP= 90∘，∴∠P90∘−∠DOP= 10∘.= 60∘","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:17:08"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:17:08"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:17:08"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:17:41"}],"detail_url":"/questions/24950","edit_url":"/questions/24950/edit","json_url":"/api/questions/24950","recheck_url":"/api/questions/24950/recheck"},{"id":24946,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[1,2],"stem":"如图，点$A,B,C 在\\(odot O\\)上，过点\\(A\\)作\\(odot O\\)的切线交\\(OC\\)的延长线于点\\(P\\)，\\(angle B = 30^circ\\)，\\(OP= 3\\)，则\\(AP\\)的长为( ) A. 3 B. \\(\\frac{3}{2}\\) C. 2√3 D. 3√3 3 2","options":[{"label":"A","text":"3"},{"label":"B","text":"\\frac{3}{2}"},{"label":"C","text":"2√3"},{"label":"D","text":"3√3 3 2"}],"answer":"D","solution":"连接OA，∵∠B = 30∘, ∴∠AOC= 2∠B = 60∘, ∵过点A作⊙O的切线交 √3 3√3 OC的延长线于点P，∴∠OAP= 90∘, ∵OP= 3, ∴AP= OP sin 60∘\\(3 \\times = =\\). 2 2","stem_html":"<div>如图，点$A,B,C<span class=\"formula-fallback\">在\\(odot O\\)上，过点\\(A\\)作\\(odot O\\)的切线交\\(OC\\)的延长线于点\\(P\\)，\\(angle B = 30^circ\\)，\\(OP= 3\\)，则\\(AP\\)的长为(     )</span><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/baaa60de-24dc-4753-9513-ecde772615b4/9be1c317f573.png\" style=\"width:180.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 3<br>B. \\(\\frac{3}{2}\\)<br>C. 2√3<br>D. 3√3 3 2</div>","answer_html":"D","solution_html":"连接OA，∵∠B = 30∘, ∴∠AOC= 2∠B = 60∘, ∵过点A作⊙O的切线交 √3 3√3 OC的延长线于点P，∴∠OAP= 90∘, ∵OP= 3, ∴AP= OP sin 60∘\\(3 \\times = =\\). 2 2","answer_missing":false,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:17:36"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:17:36"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:17:36"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T05:18:23"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T05:19:10"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T05:19:10"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T05:19:10"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T05:20:33"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-09-26T05:20:33"}],"detail_url":"/questions/24946","edit_url":"/questions/24946/edit","json_url":"/api/questions/24946","recheck_url":"/api/questions/24946/recheck"},{"id":24945,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1335.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"如图，已知\\(\\triangle ABC\\)，以\\(AB\\)为直径的\\(\\odot O\\)交\\(BC\\)于点\\(D\\)，与\\(AC\\)相切于点\\(A\\)，连接\\(OD\\)．若\\(\\angle AOD = 82^{\\circ}\\)，则\\(\\angle C\\)的度数为( ) A. 100∘ B. 82∘ C. 49∘ D. 56∘","options":[{"label":"A","text":"100∘"},{"label":"B","text":"82∘"},{"label":"C","text":"49∘"},{"label":"D","text":"56∘"}],"answer":"C","solution":"∵\\widehat{AD}=\\widehat{AD} ∴∠B=\\(\\frac{1}{2}∠AOD=41^{\\circ}\\)∵以AB为直径的⊙O与AC相切于点A ∴∠BAC=90^{\\(\\circ\\)} ∴∠C=90^{\\(\\circ\\)}-41^{\\(\\circ\\)}=49^{\\(\\circ\\)}.","stem_html":"<div>如图，已知\\(\\triangle ABC\\)，以\\(AB\\)为直径的\\(\\odot O\\)交\\(BC\\)于点\\(D\\)，与\\(AC\\)相切于点\\(A\\)，连接\\(OD\\)．若\\(\\angle AOD = 82^{\\circ}\\)，则\\(\\angle C\\)的度数为(  )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/cbb5087b-c1e9-461b-8e96-ac062249464d/0ccecb4e566d.png\" style=\"width:128.6px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 100∘<br>B. 82∘<br>C. 49∘<br>D. 56∘</div>","answer_html":"C","solution_html":"∵\\widehat{AD}=\\widehat{AD} ∴∠B=\\(\\frac{1}{2}∠AOD=41^{\\circ}\\)∵以AB为直径的⊙O与AC相切于点A ∴∠BAC=90^{\\(\\circ\\)} ∴∠C=90^{\\(\\circ\\)}-41^{\\(\\circ\\)}=49^{\\(\\circ\\)}.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:14:56"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:14:56"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:14:56"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:15:21"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T05:18:28"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:18:28"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:18:28"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T05:19:34"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T05:19:34"}],"detail_url":"/questions/24945","edit_url":"/questions/24945/edit","json_url":"/api/questions/24945","recheck_url":"/api/questions/24945/recheck"},{"id":24942,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[5,6],"stem":"如图，在\\(\\triangle ABC\\)中，以\\(BC\\)为直径的\\(\\odot O\\)，交\\(AB\\)的延长线于点\\(D\\)，交\\(AC\\)于点\\(E\\)．连接$OD, OE ，若\\(angle DOE = 130^circ\\)，则\\(angle A\\)的度数为( ) A. 45∘ B. 40∘ C. 35∘ D. 25∘","options":[{"label":"A","text":"45∘"},{"label":"B","text":"40∘"},{"label":"C","text":"35∘"},{"label":"D","text":"25∘"}],"answer":"","solution":"","stem_html":"<div>如图，在\\(\\triangle ABC\\)中，以\\(BC\\)为直径的\\(\\odot O\\)，交\\(AB\\)的延长线于点\\(D\\)，交\\(AC\\)于点\\(E\\)．连接$OD, OE<span class=\"formula-fallback\">，若\\(angle DOE = 130^circ\\)，则\\(angle A\\)的度数为( )</span><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/d29b72b7-462f-4452-85cb-778c9d9f3ff2/5ac8663b1a58.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 45∘<br>B. 40∘<br>C. 35∘<br>D. 25∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:08:47"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:08:47"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:08:47"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:09:17"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T05:12:10"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:12:10"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:12:10"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T05:12:14"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T05:12:14"}],"detail_url":"/questions/24942","edit_url":"/questions/24942/edit","json_url":"/api/questions/24942","recheck_url":"/api/questions/24942/recheck"},{"id":24943,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.667,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[6,6],"stem":"如图，OA交⊙O于点B, AC切⊙O于点C，点D在⊙O上，若∠D = 30°, ⊙O的半径为\\(\\sqrt{2}\\)cm，则线段AB的长为( ) A. 2√2cm B. √2 cm C. \\(\\sqrt{2_{2}}\\)cm D. \\(3 _{2}\\)√2 cm","options":[{"label":"A","text":"2√2cm"},{"label":"B","text":"√2 cm"},{"label":"C","text":"\\sqrt{2_{2}} cm"},{"label":"D","text":"3 _{2} √2 cm"}],"answer":"","solution":"","stem_html":"<div>如图，OA交⊙O于点B, AC切⊙O于点C，点D在⊙O上，若∠D = 30°, ⊙O的半径为\\(\\sqrt{2}\\)cm，则线段AB的长为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/64d99fc9-2815-4bb4-8f8c-160c017b4efd/324071edc12a.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 2√2cm<br>B. √2 cm<br>C. \\(\\sqrt{2_{2}}\\)cm<br>D. \\(3 _{2}\\)√2 cm</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:11:25"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:11:25"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:11:25"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T05:11:46"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T05:11:58"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:11:58"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:11:58"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T05:12:08"},{"type":"QUALITY_GATE","status":"FAIL","score":0.667,"created_at":"2026-09-26T05:12:08"}],"detail_url":"/questions/24943","edit_url":"/questions/24943/edit","json_url":"/api/questions/24943","recheck_url":"/api/questions/24943/recheck"},{"id":24934,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图是车轮侧面图当过圆心的车架,OAC 的一端落在地面上时, 与 O的另一个\\(A \\frac{AC}{AB}\\)D ,水平地面 与 O相切于点.\\(B \\frac{交点为点}{求证}\\): + 2 = \\(\\frac{(1)}{(2)}\\)A C 若AD = 2m, AB = 3m,求  O的半径.","options":[],"answer":"","solution":"(1)证明：连接?,AB?与O相切于点，\\(\\frac{OB}{ABO}\\)B  ⊥,?即 = 90,+ AOB\\(\\frac{OB}{90} \\frac{AB}{OB}\\)A =  = OC,OBC = ,AOB C = OBC +  = 2,+ 2 = 90 . C C A C (2)设  O，则OD = = rm， frac的半径为ODfracrm(2 fracOBRtABO  = + = +) ．在  中， fracOAAB fracADmOB fracrm(2 = 3, = rm,OA = + r)m ，由勾股 定理得： + =\\(OA^{2}\\)，即 + =\\(\\frac{OB^{2}}{r^{2}} \\frac{AB^{2}}{4} \\frac{r^{2}}{4} \\frac{3^{2}}{r} +\\)r)2， + 9 = + 4r +,9 = + 4, frac(24 \\(fracr^2\\)的半径为 r = 5,r = 1.25. O 1.25m．","stem_html":"<div>如图是车轮侧面图当过圆心的车架,OAC 的一端落在地面上时, 与 O的另一个\\(A \\frac{AC}{AB}\\)D ,水平地面 与 O相切于点.\\(B \\frac{交点为点}{求证}\\): + 2 = \\(\\frac{(1)}{(2)}\\)A C 若AD = 2m, AB = 3m,求  O的半径.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/6a3ca8e2-7cb2-417a-a3b0-a7d27d2889ab/a4dc7a2ccc92.png\" style=\"width:285.4px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"(1)证明：连接?,AB?与O相切于点，\\(\\frac{OB}{ABO}\\)B  ⊥,?即 = 90,+ AOB\\(\\frac{OB}{90} \\frac{AB}{OB}\\)A =  = OC,OBC = ,AOB C = OBC +  = 2,+ 2 = 90 . C C A C (2)设  O，则OD = = rm，<span class=\"formula-fallback\">frac的半径为ODfracrm(2 fracOBRtABO  = + = +)</span>．在  中，<span class=\"formula-fallback\">fracOAAB fracADmOB fracrm(2 = 3, = rm,OA = + r)m</span>，由勾股 定理得： + =\\(OA^{2}\\)，即 + =\\(\\frac{OB^{2}}{r^{2}} \\frac{AB^{2}}{4} \\frac{r^{2}}{4} \\frac{3^{2}}{r} +\\)r)2， + 9 = + 4r +,9 = + 4,<span class=\"formula-fallback\">frac(24 \\(fracr^2\\)的半径为 r = 5,r = 1.25. O 1.25m．</span>","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:07:35"},{"type":"FORMULA","status":"FAIL","score":1.0,"created_at":"2026-09-26T05:07:35"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:07:35"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:08:28"}],"detail_url":"/questions/24934","edit_url":"/questions/24934/edit","json_url":"/api/questions/24934","recheck_url":"/api/questions/24934/recheck"},{"id":24936,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"【小试1】 据史料记载，马车的发明者是4000多年前生活于夏王朝初年的奚仲，马 车的发明，是中国科技史上的一大创举．如图所示是古代马车的 侧面示意图，AB是车轮⊙ O 的直径，过圆心 O 的车架 AC 的一端点C着地时，水平地面 CD 与车轮 ⊙ O相切于点D，连接AD, BD． （1）求证：∠BDC = ∠A； （2）若tanA =\\(\\sqrt{6_{3}}\\), CB = 2 m，求车轮的半径长．","options":[],"answer":"（1）证明见解析（2）0.5m","solution":"(1)如图所示，连接OD, ∵OD = OB, ∴∠OBD = ∠ODB，∵AB是⊙O的直径，∴∠ADB = 90∘, ∴∠A + ∠OBD = 90∘，∵CD与⊙O相切于点D∴CD ⊥OD, ∴∠ODC = 90∘，∴∠CDB + ∠ODB = 90∘, ∴∠A = ∠CDB； (2)∵∠C = ∠C, ∠A = ∠CDB, ∴△CAD ∽△CDB, ∴ AC CD\\(AD _{CD}\\)= _{BC}= _{BD}∵在Rt △ADB中，tanA =\\(\\sqrt{6_{3}}\\), ∴ _{AD}=\\(\\sqrt{6_{3}}\\), ∴ BD\\(AD _{BD}\\)=\\(\\sqrt{6_{2}}\\)，又∵CB = 2m，∴_{CD}= _{2}=\\(\\sqrt{6_{2}}\\), ∴CD = √6m, ∴AC = 3m, ∴AB = AC −CB = 3 − AC CD 2=1m, ∴ 车轮的半径长为 0.5m ．","stem_html":"<div>【小试1】 据史料记载，马车的发明者是4000多年前生活于夏王朝初年的奚仲，马 车的发明，是中国科技史上的一大创举．如图所示是古代马车的 侧面示意图，AB是车轮⊙ O 的直径，过圆心 O 的车架 AC 的一端点C着地时，水平地面 CD 与车轮 ⊙ O相切于点D，连接AD, BD．<br>（1）求证：∠BDC = ∠A；<br>（2）若tanA =\\(\\sqrt{6_{3}}\\), CB = 2 m，求车轮的半径长．</div>","answer_html":"（1）证明见解析（2）0.5m","solution_html":"(1)如图所示，连接OD, ∵OD = OB, ∴∠OBD = ∠ODB，∵AB是⊙O的直径，∴∠ADB = 90∘, ∴∠A + ∠OBD = 90∘，∵CD与⊙O相切于点D∴CD ⊥OD, ∴∠ODC = 90∘，∴∠CDB + ∠ODB = 90∘, ∴∠A = ∠CDB； (2)∵∠C = ∠C, ∠A = ∠CDB, ∴△CAD ∽△CDB, ∴ AC CD\\(AD _{CD}\\)= _{BC}= _{BD}∵在Rt △ADB中，tanA =\\(\\sqrt{6_{3}}\\), ∴ _{AD}=\\(\\sqrt{6_{3}}\\), ∴ BD\\(AD _{BD}\\)=\\(\\sqrt{6_{2}}\\)，又∵CB = 2m，∴_{CD}= _{2}=\\(\\sqrt{6_{2}}\\), ∴CD = √6m, ∴AC = 3m, ∴AB = AC −CB = 3 − AC CD 2=1m, ∴ 车轮的半径长为 0.5m ．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:05:57"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:05:57"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:05:57"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:06:37"}],"detail_url":"/questions/24936","edit_url":"/questions/24936/edit","json_url":"/api/questions/24936","recheck_url":"/api/questions/24936/recheck"},{"id":24940,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，四边形ABCD是⊙O的内接四边形，∠ADC = 90°, DC = BC，直线EA与⊙ O相切于点A．若∠BCD = 128°，则∠DAE的度数为____．","options":[],"answer":"","solution":"","stem_html":"<div>如图，四边形ABCD是⊙O的内接四边形，∠ADC = 90°, DC = BC，直线EA与⊙ O相切于点A．若∠BCD = 128°，则∠DAE的度数为____．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:02:36"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:02:36"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:02:36"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T05:02:57"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T05:03:25"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T05:03:25"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T05:03:25"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T05:03:36"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T05:03:36"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.0,"created_at":"2026-09-26T05:08:52"}],"detail_url":"/questions/24940","edit_url":"/questions/24940/edit","json_url":"/api/questions/24940","recheck_url":"/api/questions/24940/recheck"},{"id":24935,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图四边形, 是  O的内接四边形点,\\(O \\frac{ABCD}{ABCD}\\)在四边形 内部过点作, O AB\\(C \\frac{的切线交}{AOB}\\)的延长线于点P,,.若 =140,\\(\\frac{连接}{ADC}\\frac{OAOB}{的度数为}\\) = 35,则 ( )\\(\\frac{BCP}{.105}\\).75.135.150 A B C D","options":[],"answer":"","solution":"由圆心角AOB = 140可得弧AB所对的  = 70．根据弦切角定理，\\(\\frac{圆周角}{切线} \\frac{ACB}{与弦}\\)CP BC的夹角BCP等于弦\\(\\frac{BC}{35}\\)所对的圆周角，即 =  = ．\\(\\frac{BCP}{180} \\frac{BAC}{ACB}\\)在 中，ABC =  − −BAC\\(\\frac{ABC}{180} =\\)−70 − 35 = 75 ．由于四边形\\(\\frac{ABCD}{180}\\)内接于圆，对角互补，所以ADC =  −ABC = 105．故选。 A","stem_html":"<div>如图四边形, 是  O的内接四边形点,\\(O \\frac{ABCD}{ABCD}\\)在四边形 内部过点作, O AB\\(C \\frac{的切线交}{AOB}\\)的延长线于点P,,.若 =140,\\(\\frac{连接}{ADC}\\frac{OAOB}{的度数为}\\) = 35,则 ( )\\(\\frac{BCP}{.105}\\).75.135.150 A B C D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/22a1865d-9e91-4ea0-969e-9783a470f14c/8c3312c9dc38.png\" style=\"width:193.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"由圆心角AOB = 140可得弧AB所对的  = 70．根据弦切角定理，\\(\\frac{圆周角}{切线} \\frac{ACB}{与弦}\\)CP BC的夹角BCP等于弦\\(\\frac{BC}{35}\\)所对的圆周角，即 =  = ．\\(\\frac{BCP}{180} \\frac{BAC}{ACB}\\)在 中，ABC =  − −BAC\\(\\frac{ABC}{180} =\\)−70 − 35 = 75 ．由于四边形\\(\\frac{ABCD}{180}\\)内接于圆，对角互补，所以ADC =  −ABC = 105．故选。 A","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:03:51"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:03:51"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:03:51"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:04:29"}],"detail_url":"/questions/24935","edit_url":"/questions/24935/edit","json_url":"/api/questions/24935","recheck_url":"/api/questions/24935/recheck"},{"id":24937,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"[小试2] 如图，四边形ABCD为⊙O的内接四边形，AB为⊙O的直径，点P在BA的延长线上，PD与⊙O相切，切点为D，若∠BCD = 130°，则∠P的大小为( ) A. 10∘ B. 40∘ C. 50∘ D. 80∘","options":[{"label":"A","text":"10∘"},{"label":"B","text":"40∘"},{"label":"C","text":"50∘"},{"label":"D","text":"80∘"}],"answer":"A","solution":"连接OD，∵四边形ABCD为⊙O的内接四边形，∠BCD = 130°∴∠OAD=180°−∠BCD = 50°, ∵OA = OD, ∴∠OAD = ∠ODA = 50°∴∠AOD=180°−∠OAD −∠ODA = 80°, ∵PD与⊙O相切∴∠ODP = 90°∴∠P = 90°−∠DOP = 10°.","stem_html":"<div>[小试2] 如图，四边形ABCD为⊙O的内接四边形，AB为⊙O的直径，点P在BA的延长线上，PD与⊙O相切，切点为D，若∠BCD = 130°，则∠P的大小为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/a8ce28c2-219c-4045-bb96-c32986a12ed2/05ef6c731bd1.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/a8ce28c2-219c-4045-bb96-c32986a12ed2/94f5ddcf84c8.png\" style=\"width:54.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 10∘<br>B. 40∘<br>C. 50∘<br>D. 80∘</div>","answer_html":"A","solution_html":"连接OD，∵四边形ABCD为⊙O的内接四边形，∠BCD = 130°∴∠OAD=180°−∠BCD = 50°, ∵OA = OD, ∴∠OAD = ∠ODA = 50°∴∠AOD=180°−∠OAD −∠ODA = 80°, ∵PD与⊙O相切∴∠ODP = 90°∴∠P = 90°−∠DOP = 10°.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:02:47"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:02:47"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:02:47"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T05:03:07"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T05:03:36"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T05:03:36"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T05:03:36"}],"detail_url":"/questions/24937","edit_url":"/questions/24937/edit","json_url":"/api/questions/24937","recheck_url":"/api/questions/24937/recheck"},{"id":24941,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，在\\(\\odot O\\)的内接四边形$ABCD 中，\\(AB\\)是直径，过点\\(D\\)的切线与直线\\(AB\\)交于点\\(P\\)，\\(angle ADP = 25^circ\\)，连接\\(OD\\)，求\\(angle BCD\\)的度数．","options":[],"answer":"","solution":"","stem_html":"<div>如图，在\\(\\odot O\\)的内接四边形$ABCD<span class=\"formula-fallback\">中，\\(AB\\)是直径，过点\\(D\\)的切线与直线\\(AB\\)交于点\\(P\\)，\\(angle ADP = 25^circ\\)，连接\\(OD\\)，求\\(angle BCD\\)的度数．</span><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/acd3186b-dff8-4191-b4a7-7cb5cf2e48ae/a4e7b8cfe778.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:03:07"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:03:07"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:03:07"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T05:03:24"}],"detail_url":"/questions/24941","edit_url":"/questions/24941/edit","json_url":"/api/questions/24941","recheck_url":"/api/questions/24941/recheck"},{"id":24939,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"板车是一种以前在街头巷尾经常能看到的人力或畜力牵引的运输工 具．它主要部分是一块平板，平板下面安装轮子．图1是板车把手端点 C着地时侧面示意图，图2是板车后尾端点E着地时侧面示意图AB为车轮⊙ O的直径，车架CE过圆心O, AE = AB，地面与车轮⊙O相 切于点 D．如图 1，连接 AD, BD，若 tan∠BDC =\\(4 _{5}\\), CD = 2.4m. （1）求证：∠ADC = ∠DBC； （2）求车轮⊙O的半径长． （3）在（1）的条件下，如图2所示，当板车后尾端点E着地时，求板车把手端点C到地面的距离．","options":[],"answer":"","solution":"","stem_html":"<div>板车是一种以前在街头巷尾经常能看到的人力或畜力牵引的运输工 具．它主要部分是一块平板，平板下面安装轮子．图1是板车把手端点 C着地时侧面示意图，图2是板车后尾端点E着地时侧面示意图AB为车轮⊙ O的直径，车架CE过圆心O, AE = AB，地面与车轮⊙O相 切于点 D．如图 1，连接 AD, BD，若 tan∠BDC =\\(4 _{5}\\), CD = 2.4m.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/210c7b4e-750c-464f-818f-ac6f5f2aed03/6d0d7a61a7ce.png\" style=\"width:566.7px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）求证：∠ADC = ∠DBC；<br>（2）求车轮⊙O的半径长．<br>（3）在（1）的条件下，如图2所示，当板车后尾端点E着地时，求板车把手端点C到地面的距离．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:02:16"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:02:16"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:02:16"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:02:34"}],"detail_url":"/questions/24939","edit_url":"/questions/24939/edit","json_url":"/api/questions/24939","recheck_url":"/api/questions/24939/recheck"},{"id":24938,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1330.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"老舍先生作品《骆驼祥子》的主人翁是一个以拉车为生的贫苦车夫．人 力车涉及了很多复杂的机械设计，如图是人力车的侧面示意图及抽象出来的几何图形，AB为车轮⊙ O的直径，过圆心O的车架AC一端点C着地时，地面CD与车轮⊙O相切于点D，连接AD, BD． （1）求证：∠BDC = ∠BAD； （2）若车架端点C到车轮与地面的接触点D之间的距离为\\(\\sqrt{6}\\)米，BC的长为2米，求车轮的半径．","options":[],"answer":"","solution":"","stem_html":"<div>老舍先生作品《骆驼祥子》的主人翁是一个以拉车为生的贫苦车夫．人 力车涉及了很多复杂的机械设计，如图是人力车的侧面示意图及抽象出来的几何图形，AB为车轮⊙ O的直径，过圆心O的车架AC一端点C着地时，地面CD与车轮⊙O相切于点D，连接AD, BD．<br>（1）求证：∠BDC = ∠BAD；<br>（2）若车架端点C到车轮与地面的接触点D之间的距离为\\(\\sqrt{6}\\)米，BC的长为2米，求车轮的半径．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T05:01:38"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T05:01:38"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T05:01:38"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T05:02:11"}],"detail_url":"/questions/24938","edit_url":"/questions/24938/edit","json_url":"/api/questions/24938","recheck_url":"/api/questions/24938/recheck"},{"id":24907,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[6,7],"stem":"如图，AB是⊙O的直径，AC是⊙O的切线，连接BD, ∠C = 30°, AB=12，则BD的长为( ) A. 6 B. \\(6\\sqrt{3}\\) C. 10 D. 10√3","options":[{"label":"A","text":"6"},{"label":"B","text":"6\\sqrt{3}"},{"label":"C","text":"10"},{"label":"D","text":"10√3"}],"answer":"","solution":"","stem_html":"<div>如图，AB是⊙O的直径，AC是⊙O的切线，连接BD, ∠C = 30°, AB=12，则BD的长为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/2f97e70c-d61e-4515-a821-0e5689fc2514/2009efbaa48d.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 6<br>B. \\(6\\sqrt{3}\\)<br>C. 10<br>D. 10√3</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:53:29"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:53:29"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:53:29"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:53:51"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T04:55:57"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:55:57"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:55:57"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T04:56:01"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T04:56:01"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T04:57:15"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:57:15"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:57:24"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:57:24"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:57:24"}],"detail_url":"/questions/24907","edit_url":"/questions/24907/edit","json_url":"/api/questions/24907","recheck_url":"/api/questions/24907/recheck"},{"id":24898,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图已知点,, 在 上,AOB = 72,\\(\\frac{AB}{O}\\frac{O}{相切切点为}\\)直线MN与,,且为弧 C C AB的中点则, 等于( )\\(\\frac{ACM}{.18 .30 .36 .72}\\)    A B C D","options":[],"answer":"","solution":"连接 : AB的中点， = 72\\(\\frac{OCC}{AOC}\\frac{为弧}{BOC} \\frac{AOB}{MN}\\) =  =   与\\(O \\frac{36}{MN} \\frac{直线}{OCM}\\)C OC. ⊥ 即 = 90\\(\\frac{相切于点}{OA}\\) = OC, = (−) / 2 =\\(72 \\frac{OCA}{OCM} \\frac{180}{OCA} \\frac{36}{90}\\) =  − = − 72 =\\(18 \\frac{ACM}{对应选项}\\)A","stem_html":"<div>如图已知点,, 在 上,AOB = 72,\\(\\frac{AB}{O}\\frac{O}{相切切点为}\\)直线MN与,,且为弧 C C AB的中点则, 等于( )\\(\\frac{ACM}{.18 .30 .36 .72}\\)    A B C D<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/fb8e2b3b-8955-4692-bf92-f1787c1d9f17/5912fcdd6a2c.png\" style=\"width:161.0px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"连接 : AB的中点， = 72\\(\\frac{OCC}{AOC}\\frac{为弧}{BOC} \\frac{AOB}{MN}\\) =  =   与\\(O \\frac{36}{MN} \\frac{直线}{OCM}\\)C OC. ⊥ 即 = 90\\(\\frac{相切于点}{OA}\\) = OC, = (−) / 2 =\\(72 \\frac{OCA}{OCM} \\frac{180}{OCA} \\frac{36}{90}\\) =  − = − 72 =\\(18 \\frac{ACM}{对应选项}\\)A","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:52:38"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:52:38"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:52:38"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:53:54"},{"type":"SOLVER","status":"PASS","score":0.7,"created_at":"2026-09-26T04:54:23"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T04:54:23"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:54:23"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T04:55:31"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T04:55:31"}],"detail_url":"/questions/24898","edit_url":"/questions/24898/edit","json_url":"/api/questions/24898","recheck_url":"/api/questions/24898/recheck"},{"id":24906,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[6,6],"stem":"如图，\\(\\triangle ABC\\)中，\\(AB = AC\\)，以底边\\(BC\\)为直径的\\(\\odot O\\)分别交\\(AB\\),\\(AC\\)于点\\(D\\),\\(E\\)，连接\\(OD\\),\\(OE\\)，若\\(\\angle A = 50^{\\circ}\\)，则\\(\\angle DOE\\)的度数是( ) A. 85∘ B. 80∘ C. 65∘ D. 50∘","options":[{"label":"A","text":"85∘"},{"label":"B","text":"80∘"},{"label":"C","text":"65∘"},{"label":"D","text":"50∘"}],"answer":"","solution":"","stem_html":"<div>如图，\\(\\triangle ABC\\)中，\\(AB = AC\\)，以底边\\(BC\\)为直径的\\(\\odot O\\)分别交\\(AB\\),\\(AC\\)于点\\(D\\),\\(E\\)，连接\\(OD\\),\\(OE\\)，若\\(\\angle A = 50^{\\circ}\\)，则\\(\\angle DOE\\)的度数是( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/52e58b64-ea45-4a5b-b622-7d9331b65e5d/13643b457181.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 85∘<br>B. 80∘<br>C. 65∘<br>D. 50∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:52:26"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:52:26"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:52:26"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:53:52"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:53:52"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:53:52"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:53:52"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:54:07"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T04:54:07"}],"detail_url":"/questions/24906","edit_url":"/questions/24906/edit","json_url":"/api/questions/24906","recheck_url":"/api/questions/24906/recheck"},{"id":24904,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，在△ABC中，BD是∠ABC的平分线，以点D为圆心的⊙D与BA相 切于点A，分别与AC, BD相交于点E, F．求证：BC是⊙D的切线．","options":[],"answer":"","solution":"","stem_html":"<div>如图，在△ABC中，BD是∠ABC的平分线，以点D为圆心的⊙D与BA相 切于点A，分别与AC, BD相交于点E, F．求证：BC是⊙D的切线．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/3d564263-8376-4993-ab9e-0f31593053de/4a1f5569682e.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.95,"created_at":"2026-09-26T04:48:55"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:48:55"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:48:55"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:49:54"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:51:48"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:51:48"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:51:48"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:52:02"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T04:52:02"}],"detail_url":"/questions/24904","edit_url":"/questions/24904/edit","json_url":"/api/questions/24904","recheck_url":"/api/questions/24904/recheck"},{"id":24902,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，AB是⊙O的切线，点C、D在⊙O上，若∠CAB = 50°，则∠D=( ) A. 40∘ B. 45∘ C. 50∘ D. 60∘","options":[{"label":"A","text":"40∘"},{"label":"B","text":"45∘"},{"label":"C","text":"50∘"},{"label":"D","text":"60∘"}],"answer":"","solution":"","stem_html":"<div>如图，AB是⊙O的切线，点C、D在⊙O上，若∠CAB = 50°，则∠D=( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/ae29b37c-4020-41ad-9b0b-c5de0400fc3a/078e013a4463.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 40∘<br>B. 45∘<br>C. 50∘<br>D. 60∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:49:12"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:49:12"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:49:12"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:50:09"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:50:58"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:50:58"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:50:58"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:51:13"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T04:51:13"}],"detail_url":"/questions/24902","edit_url":"/questions/24902/edit","json_url":"/api/questions/24902","recheck_url":"/api/questions/24902/recheck"},{"id":24896,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"证明直线是圆的切线的通用思路：","options":[],"answer":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为——若直线与圆有明确的公共点，则连接半径并证明垂直；若直线与圆没有明确的公共点，则作垂线并证明距离等于半径。","stem_html":"<div>证明直线是圆的切线的通用思路：</div>","answer_html":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution_html":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为——若直线与圆有明确的公共点，则连接半径并证明垂直；若直线与圆没有明确的公共点，则作垂线并证明距离等于半径。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:47:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:47:17"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:43"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:43"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T04:47:54"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:54"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:47:54"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T04:47:54"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:49:31"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:49:31"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:49:31"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:49:31"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:49:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:00:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:15:21"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:30:26"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:45:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:00:35"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:15:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:30:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:45:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:00:55"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/24896","edit_url":"/questions/24896/edit","json_url":"/api/questions/24896","recheck_url":"/api/questions/24896/recheck"},{"id":24884,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.962,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"证明直线是圆的切线的通用思路： __________________________________________ __________________________________________","options":[],"answer":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为——若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径。","stem_html":"<div>证明直线是圆的切线的通用思路： __________________________________________ __________________________________________</div>","answer_html":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution_html":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为——若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:44:44"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:44:44"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:44:44"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:05"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:05"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:18"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:18"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:45:18"},{"type":"QUALITY_GATE","status":"FAIL","score":0.962,"created_at":"2026-09-26T04:45:18"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:06"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:06"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:47:06"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:06"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:47:06"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:00:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:15:21"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:30:26"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:45:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:00:35"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:15:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:30:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:45:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:00:55"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/24884","edit_url":"/questions/24884/edit","json_url":"/api/questions/24884","recheck_url":"/api/questions/24884/recheck"},{"id":24889,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.962,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"证明直线是圆的切线的通用思路： __________________________________________ __________________________________________","options":[],"answer":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为——若直线与圆有明确的公共点，则连接圆心与该公共点（即半径），再证直线与该半径垂直；若直线与圆没有明确的公共点，则过圆心作直线的垂线，再证垂足到圆心的距离等于半径。","stem_html":"<div>证明直线是圆的切线的通用思路： __________________________________________ __________________________________________</div>","answer_html":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution_html":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为——若直线与圆有明确的公共点，则连接圆心与该公共点（即半径），再证直线与该半径垂直；若直线与圆没有明确的公共点，则过圆心作直线的垂线，再证垂足到圆心的距离等于半径。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:45:31"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:31"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:45:31"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:42"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:46:18"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:46:18"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:46:18"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:46:18"},{"type":"QUALITY_GATE","status":"FAIL","score":0.962,"created_at":"2026-09-26T04:46:18"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:01"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:01"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:47:01"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:47:01"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:47:01"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:00:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:15:21"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:30:26"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:45:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:00:35"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:15:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:30:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:45:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:00:55"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/24889","edit_url":"/questions/24889/edit","json_url":"/api/questions/24889","recheck_url":"/api/questions/24889/recheck"},{"id":24887,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"证明直线是圆的切线的通用思路： __________________________________________ __________________________________________","options":[],"answer":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution":"依据《核心知识点》原文第5条，该表述为教材给出的标准通用思路，分为两种情形：有公共点时连半径证垂直，无公共点时作垂线证半径。","stem_html":"<div>证明直线是圆的切线的通用思路： __________________________________________ __________________________________________</div>","answer_html":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution_html":"依据《核心知识点》原文第5条，该表述为教材给出的标准通用思路，分为两种情形：有公共点时连半径证垂直，无公共点时作垂线证半径。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:45:02"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:02"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:45:02"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T04:45:19"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:47"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:47"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:45:47"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:47"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T04:45:47"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:46:29"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:46:29"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:46:29"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:46:29"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:00:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:15:21"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:30:26"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:45:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:00:35"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:15:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:30:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:45:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:00:55"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/24887","edit_url":"/questions/24887/edit","json_url":"/api/questions/24887","recheck_url":"/api/questions/24887/recheck"},{"id":24885,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1325.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"圆的的切线垂直于______________________","options":[],"answer":"过切点的半径","solution":"根据圆的切线性质定理：圆的切线垂直于过切点的半径。这是圆的基本几何性质之一，用于判断切线方向或证明垂直关系。","stem_html":"<div>圆的的切线垂直于______________________</div>","answer_html":"过切点的半径","solution_html":"根据圆的切线性质定理：圆的切线垂直于过切点的半径。这是圆的基本几何性质之一，用于判断切线方向或证明垂直关系。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:44:48"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:44:48"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:44:48"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T04:45:15"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:24"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:24"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:24"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T04:45:29"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T04:45:29"}],"detail_url":"/questions/24885","edit_url":"/questions/24885/edit","json_url":"/api/questions/24885","recheck_url":"/api/questions/24885/recheck"},{"id":24868,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1320.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"【小试2】 如图，AB为⊙O的直径，CD与⊙ O相切于点C，交AB的延长线于点D，且CA = CD．若BD = 3，则⊙ O半径长为( )\\(\\frac{(A)2}{(B)3}\\) C. 3√3 D. 2√3","options":[{"label":"C","text":"3√3"},{"label":"D","text":"2√3"}],"answer":"B","solution":"∵AB 为 ⊙O 的直径，∴∠ACB = 90∘, ∴∠A + ∠ABC = 90∘, 如图，连接 OC，∵CD 与 ⊙O 相切于点 C，∴ ∠OCD = 90∘, ∴∠DCB + ∠OCB=90∘, ∵OB = OC，∴∠BCD = ∠A，∵CA = CD，∴∠A = ∠D，∴∠BCD=∠D，∴ ∠ABC = 2∠D = 2∠A ∴3∠A = 90∘, ∴∠A = 30∘, ∵∠BCD=∠D，∴BC = BD = 3, ∴AB = 2BC = 6, ∴⊙ O半径长为 3.","stem_html":"<div>【小试2】 如图，AB为⊙O的直径，CD与⊙ O相切于点C，交AB的延长线于点D，且CA = CD．若BD = 3，则⊙ O半径长为( )\\(\\frac{(A)2}{(B)3}\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/870a2eda-115b-44f0-ad57-0fcd39f07e6c/dc5d0ac19c23.png\" style=\"width:302.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>C. 3√3<br>D. 2√3</div>","answer_html":"B","solution_html":"∵AB 为 ⊙O 的直径，∴∠ACB = 90∘, ∴∠A + ∠ABC = 90∘, 如图，连接 OC，∵CD 与 ⊙O 相切于点 C，∴ ∠OCD = 90∘, ∴∠DCB + ∠OCB=90∘, ∵OB = OC，∴∠BCD = ∠A，∵CA = CD，∴∠A = ∠D，∴∠BCD=∠D，∴ ∠ABC = 2∠D = 2∠A ∴3∠A = 90∘, ∴∠A = 30∘, ∵∠BCD=∠D，∴BC = BD = 3, ∴AB = 2BC = 6, ∴⊙ O半径长为 3.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:41:49"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:41:49"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:41:49"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:42:51"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:43:39"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:43:39"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:43:39"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T04:44:13"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T04:44:13"}],"detail_url":"/questions/24868","edit_url":"/questions/24868/edit","json_url":"/api/questions/24868","recheck_url":"/api/questions/24868/recheck"},{"id":24872,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.863,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1320.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，AB是⊙O的直径，C是AB延长线上一点，CD切⊙O于点D, E是⊙O一点，连接DE, BE，若AB = 4, ∠E = 30°，则CD = ( ) A. 3√3 B. 4 C. 2√3 D. 3","options":[{"label":"A","text":"3√3"},{"label":"B","text":"4"},{"label":"C","text":"2√3"},{"label":"D","text":"3"}],"answer":"","solution":"","stem_html":"<div>如图，AB是⊙O的直径，C是AB延长线上一点，CD切⊙O于点D, E是⊙O一点，连接DE, BE，若AB = 4, ∠E = 30°，则CD = ( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/4bcbf34b-4bb0-460a-a7ba-0c478af4b262/f3e01ada9060.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 3√3<br>B. 4<br>C. 2√3<br>D. 3</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:38:54"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:38:54"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:38:54"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:39:26"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:39:26"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:40:08"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:40:08"},{"type":"COHERENCE","status":"FAIL","score":0.6,"created_at":"2026-09-26T04:40:25"},{"type":"QUALITY_GATE","status":"FAIL","score":0.863,"created_at":"2026-09-26T04:40:25"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:43:21"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:43:21"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:43:53"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:43:53"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:43:53"}],"detail_url":"/questions/24872","edit_url":"/questions/24872/edit","json_url":"/api/questions/24872","recheck_url":"/api/questions/24872/recheck"},{"id":24873,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1320.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，已知\\(\\angle ABC = 30^{\\circ}\\)，以O为圆心、\\(2\\,\\mathrm{cm}\\)为半径作\\(\\odot O\\)，使圆心O在BC边上移动，则当OB = ______\\(\\mathrm{cm}\\)时，\\(\\odot O\\)与AB相切.","options":[],"answer":"","solution":"","stem_html":"<div>如图，已知\\(\\angle ABC = 30^{\\circ}\\)，以O为圆心、\\(2\\,\\mathrm{cm}\\)为半径作\\(\\odot O\\)，使圆心O在BC边上移动，则当OB = ______\\(\\mathrm{cm}\\)时，\\(\\odot O\\)与AB相切.</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:38:40"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:38:40"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:38:40"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:38:50"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:40:10"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:40:10"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:40:10"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:40:24"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T04:40:24"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T04:42:07"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:42:07"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T04:42:54"},{"type":"SYMBOLIC","status":"PASS","score":0.9,"created_at":"2026-09-26T04:42:54"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T04:42:54"}],"detail_url":"/questions/24873","edit_url":"/questions/24873/edit","json_url":"/api/questions/24873","recheck_url":"/api/questions/24873/recheck"},{"id":24870,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1320.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，在\\(\\triangle ABC\\)中，D是BC边上的一点，以AD为直径的\\(\\odot O\\)交AC于点E，连接DE．若\\(\\odot O\\)与BC相切于点D，\\(\\angle ADE = 55^{\\circ}\\)，则\\(\\angle C\\)的度数为( ) A. 55∘ B. 50∘ C. 45∘ D. 40∘","options":[{"label":"A","text":"55∘"},{"label":"B","text":"50∘"},{"label":"C","text":"45∘"},{"label":"D","text":"40∘"}],"answer":"","solution":"","stem_html":"<div>如图，在\\(\\triangle ABC\\)中，D是BC边上的一点，以AD为直径的\\(\\odot O\\)交AC于点E，连接DE．若\\(\\odot O\\)与BC相切于点D，\\(\\angle ADE = 55^{\\circ}\\)，则\\(\\angle C\\)的度数为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/b447b4fa-893f-437a-8103-cd9a7c6e92ba/c5aec8cdd0bd.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 55∘<br>B. 50∘<br>C. 45∘<br>D. 40∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:36:09"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:36:09"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:36:09"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:36:44"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:36:44"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:37:28"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:37:28"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:37:44"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T04:37:44"}],"detail_url":"/questions/24870","edit_url":"/questions/24870/edit","json_url":"/api/questions/24870","recheck_url":"/api/questions/24870/recheck"},{"id":24869,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1320.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，已知△ABC，以AB为直径的⊙O交BC于点D，与AC相切于点A，连接OD．若∠AOD = 70°，则∠C的度数为( ) A. 52∘ B. 55∘ C. 35∘ D. 44∘","options":[{"label":"A","text":"52∘"},{"label":"B","text":"55∘"},{"label":"C","text":"35∘"},{"label":"D","text":"44∘"}],"answer":"","solution":"","stem_html":"<div>如图，已知△ABC，以AB为直径的⊙O交BC于点D，与AC相切于点A，连接OD．若∠AOD = 70°，则∠C的度数为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/b1bffc16-4547-40b5-9189-f1893204a903/8ca479735a6a.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 52∘<br>B. 55∘<br>C. 35∘<br>D. 44∘</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:34:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:34:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:34:50"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:35:12"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:40:10"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:40:10"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:40:10"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:40:22"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T04:40:22"}],"detail_url":"/questions/24869","edit_url":"/questions/24869/edit","json_url":"/api/questions/24869","recheck_url":"/api/questions/24869/recheck"},{"id":24867,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.933,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1320.pdf","job_source":"人教版.zip","pages":[2,3],"stem":"【小试1】 如图，以 AB 为直径的半圆 O 交 BC 于点 D，已知 AC 与 ⊙O 相切于点 A，若∠AOD = 60°，则∠C 的度数为( ) A. 30∘ B. 60∘ C. 45∘ D. 75∘","options":[{"label":"A","text":"30∘"},{"label":"B","text":"60∘"},{"label":"C","text":"45∘"},{"label":"D","text":"75∘"}],"answer":"B","solution":"∵AD = AD, ∠AOD = 60° ∴∠B =\\(\\frac{1}{2}∠AOD = 30°\\). ∵以AB为直径的⊙O与AC相切于点A，∴∠BAC = 90° ∴∠C = 90°−30°= 60°.","stem_html":"<div>【小试1】 如图，以 AB 为直径的半圆 O 交 BC 于点 D，已知 AC 与 ⊙O 相切于点 A，若∠AOD = 60°，则∠C 的度数为( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/8c6c5528-7847-450f-8a29-88999725c746/2a9d99c12f9c.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 30∘<br>B. 60∘<br>C. 45∘<br>D. 75∘</div>","answer_html":"B","solution_html":"∵AD = AD, ∠AOD = 60° ∴∠B =\\(\\frac{1}{2}∠AOD = 30°\\). ∵以AB为直径的⊙O与AC相切于点A，∴∠BAC = 90° ∴∠C = 90°−30°= 60°.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:35:31"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:35:31"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:35:31"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:35:54"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:38:16"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:38:16"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:38:16"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:38:53"},{"type":"QUALITY_GATE","status":"FAIL","score":0.933,"created_at":"2026-09-26T04:38:53"}],"detail_url":"/questions/24867","edit_url":"/questions/24867/edit","json_url":"/api/questions/24867","recheck_url":"/api/questions/24867/recheck"},{"id":24871,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.917,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1320.pdf","job_source":"人教版.zip","pages":[4,5],"stem":"如图，已知\\(\\angle AOB = 30^{\\circ}\\)，\\(\\odot O\\)的半径为3．点P在射线OB上，\\(\\odot P\\)的半径为r．如果直线OA与\\(\\odot P\\)相切，且\\(\\odot P\\)与\\(\\odot O\\)相交，那么r的值可以是( )\\(\\frac{(A)4}{(B)3}\\frac{(C)2}{(D)1}\\)","options":[],"answer":"","solution":"","stem_html":"<div>如图，已知\\(\\angle AOB = 30^{\\circ}\\)，\\(\\odot O\\)的半径为3．点P在射线OB上，\\(\\odot P\\)的半径为r．如果直线OA与\\(\\odot P\\)相切，且\\(\\odot P\\)与\\(\\odot O\\)相交，那么r的值可以是( )\\(\\frac{(A)4}{(B)3}\\frac{(C)2}{(D)1}\\)<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/cbac3584-67f0-4737-9b08-3e9b0802989d/fdf6eefbbb1e.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:36:05"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:36:05"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:36:05"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:36:26"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:38:00"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:38:00"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:38:00"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:38:09"},{"type":"QUALITY_GATE","status":"FAIL","score":0.917,"created_at":"2026-09-26T04:38:09"}],"detail_url":"/questions/24871","edit_url":"/questions/24871/edit","json_url":"/api/questions/24871","recheck_url":"/api/questions/24871/recheck"},{"id":24856,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1320.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"看到切线先连________，构造________","options":[],"answer":"圆心;直角三角形","solution":"依据《核心知识点》第3条：看到切线先连圆心和切点，构造直角三角形。","stem_html":"<div>看到切线先连________，构造________</div>","answer_html":"圆心;直角三角形","solution_html":"依据《核心知识点》第3条：看到切线先连圆心和切点，构造直角三角形。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:32:11"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:32:11"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:32:11"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:32:24"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:32:24"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T04:32:38"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:32:38"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T04:32:52"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T04:32:52"}],"detail_url":"/questions/24856","edit_url":"/questions/24856/edit","json_url":"/api/questions/24856","recheck_url":"/api/questions/24856/recheck"},{"id":24838,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.9,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1315.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图，点C在以AB为直径的半圆上AB = 6, ∠ABC= 30∘，点D在线段 A B上运动，点E与点D关于AC对称，DF ⊥ DE于点D，并交EC的延长 线于点F，当AD长度为____ 时，EF与半圆相切． 解答题，第一题8分，第二题10分，第三题10分","options":[],"answer":"\\(\\frac{3}{2}\\)或1.5","solution":"当AD=\\(\\frac{3}{2}\\)时，EF与半圆相切．连接OC,CD,∵ AB为 ⊙ O直径,∴ ∠ACB= 90^{\\(\\circ\\)}, ∵∠ABC= 30^{\\(\\circ\\)}, ∴∠CAB = 60^{\\(\\circ\\)}. ∵OA = OC, ∴△AOC是等边三角形，所 以∠ACO = 60^{\\(\\circ\\)}, ∵AD =\\(\\frac{3}{2},OA= 3,∴\\)OD=OA− AD= 3 −\\(\\frac{3}{2} = \\frac{3}{2},∴\\)AD= OD,∴ ∠ACD=\\(\\frac{1}{2}\\)∠ACO = 30^{\\(\\circ\\)}, ∵点E与点D关于AC对称, ∴∠ECA = ∠ACD= = 30^{\\(\\circ\\)}, ∴∠OCE= ∠ECA + ∠ACO = 90^{\\(\\circ\\)}, ∴OC⊥EF, ∵OC是⊙O的半 径,∴ EF与半 ⊙ O相切,∴ 当AD=\\(\\frac{3}{2}\\)时,EF与半圆相切.故答案为\\(\\frac{3}{2}\\)．","stem_html":"<div>如图，点C在以AB为直径的半圆上AB = 6, ∠ABC= 30∘，点D在线段 A B上运动，点E与点D关于AC对称，DF ⊥ DE于点D，并交EC的延长 线于点F，当AD长度为____ 时，EF与半圆相切． 解答题，第一题8分，第二题10分，第三题10分<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/c26e4663-f585-4895-90f3-5f8cdf27f731/f92002ae9762.png\" style=\"width:180.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"\\(\\frac{3}{2}\\)或1.5","solution_html":"当AD=\\(\\frac{3}{2}\\)时，EF与半圆相切．连接OC,CD,∵ AB为 ⊙ O直径,∴ ∠ACB= 90^{\\(\\circ\\)}, ∵∠ABC= 30^{\\(\\circ\\)}, ∴∠CAB = 60^{\\(\\circ\\)}. ∵OA = OC, ∴△AOC是等边三角形，所 以∠ACO = 60^{\\(\\circ\\)}, ∵AD =\\(\\frac{3}{2},OA= 3,∴\\)OD=OA− AD= 3 −\\(\\frac{3}{2} = \\frac{3}{2},∴\\)AD= OD,∴ ∠ACD=\\(\\frac{1}{2}\\)∠ACO = 30^{\\(\\circ\\)}, ∵点E与点D关于AC对称, ∴∠ECA = ∠ACD= = 30^{\\(\\circ\\)}, ∴∠OCE= ∠ECA + ∠ACO = 90^{\\(\\circ\\)}, ∴OC⊥EF, ∵OC是⊙O的半 径,∴ EF与半 ⊙ O相切,∴ 当AD=\\(\\frac{3}{2}\\)时,EF与半圆相切.故答案为\\(\\frac{3}{2}\\)．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:28:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:28:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:28:50"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:29:02"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:30:30"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:30:30"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:30:30"},{"type":"COHERENCE","status":"FAIL","score":0.85,"created_at":"2026-09-26T04:31:03"},{"type":"QUALITY_GATE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:31:03"}],"detail_url":"/questions/24838","edit_url":"/questions/24838/edit","json_url":"/api/questions/24838","recheck_url":"/api/questions/24838/recheck"},{"id":24837,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.913,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1315.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"如图,\\(AB\\)为\\(\\odot O\\)的直径,\\(AB=1\\mathrm{cm}\\),\\(BC=\\sqrt{2}\\mathrm{cm}\\),当\\(AC=\\)____\\(\\mathrm{cm}\\)时,直线\\(AC\\)与\\(\\odot O\\)相切．","options":[],"answer":"1","solution":"当\\(\\angle BAC = 90^{\\circ}\\)时，直线\\(AC\\)与\\(\\odot O\\)相切，\\(\\therefore AC = \\sqrt{BC^{2} - AB^{2}} = \\sqrt{(\\sqrt{2})^{2} - 1^{2}} = 1 (\\mathrm{cm})\\)，故答案为1．\\(\\frac{3}{2}\\)或1.5","stem_html":"<div>如图,\\(AB\\)为\\(\\odot O\\)的直径,\\(AB=1\\mathrm{cm}\\),\\(BC=\\sqrt{2}\\mathrm{cm}\\),当\\(AC=\\)____\\(\\mathrm{cm}\\)时,直线\\(AC\\)与\\(\\odot O\\)相切．<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/1f549971-f19f-46c1-9c90-a3d6b0736e23/24990edc4654.png\" style=\"width:154.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"1","solution_html":"当\\(\\angle BAC = 90^{\\circ}\\)时，直线\\(AC\\)与\\(\\odot O\\)相切，\\(\\therefore AC = \\sqrt{BC^{2} - AB^{2}} = \\sqrt{(\\sqrt{2})^{2} - 1^{2}} = 1 (\\mathrm{cm})\\)，故答案为1．\\(\\frac{3}{2}\\)或1.5","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:22:12"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:22:12"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:22:12"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:22:30"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:22:56"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:22:56"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:22:56"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T04:23:39"},{"type":"QUALITY_GATE","status":"FAIL","score":0.913,"created_at":"2026-09-26T04:23:39"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:25:08"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:25:08"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:26:38"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:26:38"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:26:38"}],"detail_url":"/questions/24837","edit_url":"/questions/24837/edit","json_url":"/api/questions/24837","recheck_url":"/api/questions/24837/recheck"},{"id":24832,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.75,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1315.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"一个圆的半径是9cm．如果圆心与直线上一点之间的距离是9cm，那么 这条直线和这个圆的位置关系是( ) A. 相切 B. 相交 C. 相交或相切 D. 相离 填空题，每题6分","options":[{"label":"A","text":"相切"},{"label":"B","text":"相交"},{"label":"C","text":"相交或相切"},{"label":"D","text":"相离 填空题，每题6分"}],"answer":"C","solution":"由题意知，\\(r=9\\,\\mathrm{cm}\\)，由圆心与直线上一点之间的距离是\\(9\\,\\mathrm{cm}\\)可知，圆心到直线的距离\\(d\\leq9\\,\\mathrm{cm}\\)．\\because\\(d\\leq r\\)，\\therefore 这条直线和这个圆的位置关系为相切或相交．故选C．","stem_html":"<div>一个圆的半径是9cm．如果圆心与直线上一点之间的距离是9cm，那么 这条直线和这个圆的位置关系是(      )<br>A. 相切<br>B. 相交<br>C. 相交或相切<br>D. 相离 填空题，每题6分</div>","answer_html":"C","solution_html":"由题意知，\\(r=9\\,\\mathrm{cm}\\)，由圆心与直线上一点之间的距离是\\(9\\,\\mathrm{cm}\\)可知，圆心到直线的距离\\(d\\leq9\\,\\mathrm{cm}\\)．\\because\\(d\\leq r\\)，\\therefore 这条直线和这个圆的位置关系为相切或相交．故选C．","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:20:41"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:20:41"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:20:41"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:21:04"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:21:04"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T04:22:18"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:22:18"},{"type":"COHERENCE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:22:43"},{"type":"QUALITY_GATE","status":"FAIL","score":0.75,"created_at":"2026-09-26T04:22:43"}],"detail_url":"/questions/24832","edit_url":"/questions/24832/edit","json_url":"/api/questions/24832","recheck_url":"/api/questions/24832/recheck"},{"id":24826,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1310.pdf","job_source":"人教版.zip","pages":[6,7],"stem":"如图，在Rt △ABC中，∠C = 90°, ∠B = 30°, BC =\\(4\\,\\mathrm{cm}\\)，以点C为圆心，以\\(3\\,\\mathrm{cm}\\)的长为半径作圆，则⊙C与AB的位置关系是( ) A. 相离 B. 相切 C. 相交 D. 相切或相交","options":[{"label":"A","text":"相离"},{"label":"B","text":"相切"},{"label":"C","text":"相交"},{"label":"D","text":"相切或相交"}],"answer":"","solution":"","stem_html":"<div>如图，在Rt △ABC中，∠C = 90°, ∠B = 30°, BC =\\(4\\,\\mathrm{cm}\\)，以点C为圆心，以\\(3\\,\\mathrm{cm}\\)的长为半径作圆，则⊙C与AB的位置关系是( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/067f534b-70c3-4f14-80f1-2f1596c595e9/6f6658509d94.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 相离<br>B. 相切<br>C. 相交<br>D. 相切或相交</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:14:30"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:14:30"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:14:30"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:15:00"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:15:01"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:15:01"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:15:01"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:15:16"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T04:15:16"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T04:16:45"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:16:45"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T04:17:35"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:17:35"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:17:35"}],"detail_url":"/questions/24826","edit_url":"/questions/24826/edit","json_url":"/api/questions/24826","recheck_url":"/api/questions/24826/recheck"},{"id":24821,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1310.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"马老师带领同学们复习《圆》的内容时, 展示出如下内容：“如图,△ABC内接于⊙ O，直径AB的长为6，过点C的切线交AB的延长线于点D. ”马老师要求同学们在此基础上添加一个条件编制一道题目，并解答问题. （1）若添加条件“\\(\\angle D = 30^{\\circ}\\)”，则AD的长为_____； （2）小亮说：\"我添加的条件是\\(\\angle A = 30^{\\circ}\\)，可以得到\\(AC = DC\\)\"，你认为小亮的说法是否正确？请说明理由．","options":[],"answer":"","solution":"","stem_html":"<div>马老师带领同学们复习《圆》的内容时, 展示出如下内容：“如图,△ABC内接于⊙ O，直径AB的长为6，过点C的切线交AB的延长线于点D. ”马老师要求同学们在此基础上添加一个条件编制一道题目，并解答问题.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/fc05b89e-3212-43f2-ad40-2ed94fb048e9/7323b2ca05e1.png\" style=\"width:302.3px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）若添加条件“\\(\\angle D = 30^{\\circ}\\)”，则AD的长为_____；<br>（2）小亮说：\"我添加的条件是\\(\\angle A = 30^{\\circ}\\)，可以得到\\(AC = DC\\)\"，你认为小亮的说法是否正确？请说明理由．</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:11:09"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:11:09"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:11:09"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:11:39"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:14:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:14:38"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:14:38"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:14:57"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T04:14:57"},{"type":"SOLVER","status":"WARN","score":0.4,"created_at":"2026-09-26T04:16:56"},{"type":"CRITIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:16:56"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.5,"created_at":"2026-09-26T04:16:56"}],"detail_url":"/questions/24821","edit_url":"/questions/24821/edit","json_url":"/api/questions/24821","recheck_url":"/api/questions/24821/recheck"},{"id":24815,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1310.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"证明直线是圆的切线的通用思路：","options":[],"answer":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution":"根据《核心知识点》第5条，证明直线是圆的切线的通用思路分为两种情况：当直线与圆有明确的公共点时，连接圆心和该公共点（即半径），然后证明直线与该半径垂直；当直线与圆没有明确的公共点时，过圆心作直线的垂线，然后证明垂足到圆心的距离等于半径。","stem_html":"<div>证明直线是圆的切线的通用思路：</div>","answer_html":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution_html":"根据《核心知识点》第5条，证明直线是圆的切线的通用思路分为两种情况：当直线与圆有明确的公共点时，连接圆心和该公共点（即半径），然后证明直线与该半径垂直；当直线与圆没有明确的公共点时，过圆心作直线的垂线，然后证明垂足到圆心的距离等于半径。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:08:50"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:08:50"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:08:50"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T04:09:08"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:09:39"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:09:39"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:09:39"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:09:39"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T04:09:39"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:10:36"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:10:36"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:10:36"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:10:36"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:10:36"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:15:02"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:30:06"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:45:11"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:00:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:15:21"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:30:26"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:45:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:00:35"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:15:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:30:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:45:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:00:55"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/24815","edit_url":"/questions/24815/edit","json_url":"/api/questions/24815","recheck_url":"/api/questions/24815/recheck"},{"id":24806,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.962,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1310.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"证明直线是圆的切线的通用思路：","options":[],"answer":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为——若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径。","stem_html":"<div>证明直线是圆的切线的通用思路：</div>","answer_html":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution_html":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为——若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:06:54"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:06:54"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:06:54"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:13"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:13"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:30"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:30"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:07:30"},{"type":"QUALITY_GATE","status":"FAIL","score":0.962,"created_at":"2026-09-26T04:07:30"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:10:04"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:10:04"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:10:04"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:10:04"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:10:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:15:02"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:30:06"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:45:11"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:00:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:15:21"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:30:26"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:45:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:00:35"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:15:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:30:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:45:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:00:55"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/24806","edit_url":"/questions/24806/edit","json_url":"/api/questions/24806","recheck_url":"/api/questions/24806/recheck"},{"id":24802,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.712,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1310.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"证明直线是圆的切线的通用思路：","options":[],"answer":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径.","solution":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为，当直线与圆有明确公共点时，连接圆心与该公共点得到半径，再证直线与该半径垂直；当直线与圆无明确公共点时，先过圆心作直线的垂线，再证垂足到圆心的距离等于半径.","stem_html":"<div>证明直线是圆的切线的通用思路：</div>","answer_html":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径.","solution_html":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为，当直线与圆有明确公共点时，连接圆心与该公共点得到半径，再证直线与该半径垂直；当直线与圆无明确公共点时，先过圆心作直线的垂线，再证垂足到圆心的距离等于半径.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:06:20"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:06:20"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:06:20"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:06:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:06:38"},{"type":"VISION","status":"FAIL","score":0.0,"created_at":"2026-09-26T04:07:13"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:07:13"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:13"},{"type":"QUALITY_GATE","status":"FAIL","score":0.712,"created_at":"2026-09-26T04:07:13"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:09:16"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:09:16"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:09:16"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:09:16"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:09:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:15:02"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:30:06"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:45:11"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:00:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:15:21"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:30:26"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:45:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:00:35"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:15:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:30:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:45:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:00:55"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/24802","edit_url":"/questions/24802/edit","json_url":"/api/questions/24802","recheck_url":"/api/questions/24802/recheck"},{"id":24805,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.913,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1310.pdf","job_source":"人教版.zip","pages":[1,1],"stem":"证明直线是圆的切线的通用思路：","options":[],"answer":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为，当直线与圆有明确公共点时，连接圆心与该公共点得到半径，再证直线与该半径垂直；当直线与圆无明确公共点时，则过圆心向直线作垂线段，再证该垂线段长度等于半径。","stem_html":"<div>证明直线是圆的切线的通用思路：</div>","answer_html":"若直线与圆有明确的公共点，就连半径，证明垂直；若直线与圆没有明确的公共点，就作垂线，证明半径","solution_html":"依据《核心知识点》第5条：证明直线是圆的切线的通用思路为，当直线与圆有明确公共点时，连接圆心与该公共点得到半径，再证直线与该半径垂直；当直线与圆无明确公共点时，则过圆心向直线作垂线段，再证该垂线段长度等于半径。","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:06:27"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:06:27"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:06:27"},{"type":"VISION","status":"FAIL","score":0.8,"created_at":"2026-09-26T04:06:40"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:19"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:19"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:19"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:07:19"},{"type":"QUALITY_GATE","status":"FAIL","score":0.913,"created_at":"2026-09-26T04:07:19"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:56"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:56"},{"type":"COHERENCE","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:07:56"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:07:56"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T04:07:56"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:15:02"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:30:06"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T04:45:11"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:00:16"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:15:21"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:30:26"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T05:45:31"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:00:35"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:15:40"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:30:45"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T06:45:50"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:00:55"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:16:00"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:31:04"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T07:46:09"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:01:14"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:16:19"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:31:24"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T08:46:29"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:01:34"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:16:39"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:31:44"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T09:46:49"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:01:54"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:16:58"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:32:03"},{"type":"RETRO_REPAIR","status":"FAIL","score":0.3,"created_at":"2026-09-26T10:47:08"}],"detail_url":"/questions/24805","edit_url":"/questions/24805/edit","json_url":"/api/questions/24805","recheck_url":"/api/questions/24805/recheck"},{"id":24789,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1305.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"已知\\(\\angle ABC = 60^{\\circ}\\)，点\\(O\\)在\\(\\angle ABC\\)的平分线上，\\(OB = 5\\,\\mathrm{cm}\\)，以点\\(O\\)为圆心，\\(2\\,\\mathrm{cm}\\)为半径作\\(\\odot O\\)，则\\(\\odot O\\)与\\(BC\\)的位置关系是( ) A. 相离 B. 相交 C. 相切 D. 不确定","options":[{"label":"A","text":"相离"},{"label":"B","text":"相交"},{"label":"C","text":"相切"},{"label":"D","text":"不确定"}],"answer":"","solution":"","stem_html":"<div>已知\\(\\angle ABC = 60^{\\circ}\\)，点\\(O\\)在\\(\\angle ABC\\)的平分线上，\\(OB = 5\\,\\mathrm{cm}\\)，以点\\(O\\)为圆心，\\(2\\,\\mathrm{cm}\\)为半径作\\(\\odot O\\)，则\\(\\odot O\\)与\\(BC\\)的位置关系是( )<br>A. 相离<br>B. 相交<br>C. 相切<br>D. 不确定</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T03:59:42"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:59:42"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:59:42"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:00:03"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T04:00:45"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:00:45"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:00:45"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:01:06"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T04:01:06"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T04:01:36"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:01:36"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T04:02:33"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T04:02:33"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.8,"created_at":"2026-09-26T04:02:33"}],"detail_url":"/questions/24789","edit_url":"/questions/24789/edit","json_url":"/api/questions/24789","recheck_url":"/api/questions/24789/recheck"},{"id":24790,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.912,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1305.pdf","job_source":"人教版.zip","pages":[3,4],"stem":"已知\\(\\triangle ABC\\)中，\\(AB = AC = 6\\,\\mathrm{cm}\\)，\\(BC = 8\\,\\mathrm{cm}\\)，以点\\(A\\)为圆心，以\\(4\\,\\mathrm{cm}\\)长为半径作圆，则\\(\\odot A\\)与\\(BC\\)的位置关系是( ) A. 相离 B. 相切 C. 相交 D. 外离","options":[{"label":"A","text":"相离"},{"label":"B","text":"相切"},{"label":"C","text":"相交"},{"label":"D","text":"外离"}],"answer":"","solution":"","stem_html":"<div>已知\\(\\triangle ABC\\)中，\\(AB = AC = 6\\,\\mathrm{cm}\\)，\\(BC = 8\\,\\mathrm{cm}\\)，以点\\(A\\)为圆心，以\\(4\\,\\mathrm{cm}\\)长为半径作圆，则\\(\\odot A\\)与\\(BC\\)的位置关系是( )<br>A. 相离<br>B. 相切<br>C. 相交<br>D. 外离</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T04:00:39"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T04:00:39"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T04:00:39"},{"type":"SOLVER","status":"PASS","score":0.7,"created_at":"2026-09-26T04:01:16"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T04:01:16"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T04:01:26"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T04:01:26"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T04:01:51"},{"type":"QUALITY_GATE","status":"FAIL","score":0.912,"created_at":"2026-09-26T04:01:51"}],"detail_url":"/questions/24790","edit_url":"/questions/24790/edit","json_url":"/api/questions/24790","recheck_url":"/api/questions/24790/recheck"},{"id":24761,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1300.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"如图，在Rt △ABC中，∠ACB = 90°, ∠A = 30°, CD是AB边上的高，AB=4，若圆D是以点D为圆心，1.4为半径的圆，那么圆D与直线AC的关系是( ) A. 相切 B. 相离 C. 相交 D. 不能确定","options":[{"label":"A","text":"相切"},{"label":"B","text":"相离"},{"label":"C","text":"相交"},{"label":"D","text":"不能确定"}],"answer":"","solution":"","stem_html":"<div>如图，在Rt △ABC中，∠ACB = 90°, ∠A = 30°, CD是AB边上的高，AB=4，若圆D是以点D为圆心，1.4为半径的圆，那么圆D与直线AC的关系是( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/feb756ee-a0c0-4923-88fe-f9446477b434/03c6bfa1c651.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 相切<br>B. 相离<br>C. 相交<br>D. 不能确定</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T03:49:28"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:49:28"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:49:28"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T03:49:56"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T03:50:39"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:50:39"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T03:50:39"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:50:55"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T03:50:55"},{"type":"SOLVER","status":"PASS","score":0.95,"created_at":"2026-09-26T03:51:38"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:51:38"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T03:54:22"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:54:22"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:54:22"}],"detail_url":"/questions/24761","edit_url":"/questions/24761/edit","json_url":"/api/questions/24761","recheck_url":"/api/questions/24761/recheck"},{"id":24758,"job_id":3,"qa_status":"QUARANTINED","question_type":"single_choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.925,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1300.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"如图，在Rt\\(\\triangle ABC\\)中，\\(\\angle C = 90^{\\circ}\\),\\(\\angle B = 30^{\\circ}\\),\\(BC = 4\\,\\mathrm{cm}\\)，以点C为圆心，以\\(3\\,\\mathrm{cm}\\)的长为半径作圆，则\\(\\odot C\\)与AB的位置关系是( ) A. 相离 B. 相切 C. 相交 D. 相切或相交","options":[{"label":"A","text":"相离"},{"label":"B","text":"相切"},{"label":"C","text":"相交"},{"label":"D","text":"相切或相交"}],"answer":"","solution":"","stem_html":"<div>如图，在Rt\\(\\triangle ABC\\)中，\\(\\angle C = 90^{\\circ}\\),\\(\\angle B = 30^{\\circ}\\),\\(BC = 4\\,\\mathrm{cm}\\)，以点C为圆心，以\\(3\\,\\mathrm{cm}\\)的长为半径作圆，则\\(\\odot C\\)与AB的位置关系是( )<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/4c99dabd-2ed0-4ac0-9762-b427c74434f0/0500563e5ee9.png\" style=\"width:264.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>A. 相离<br>B. 相切<br>C. 相交<br>D. 相切或相交</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T03:49:17"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:49:17"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:49:17"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T03:50:09"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:50:09"},{"type":"VISION","status":"PASS","score":1.0,"created_at":"2026-09-26T03:50:19"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T03:50:19"},{"type":"COHERENCE","status":"FAIL","score":0.8,"created_at":"2026-09-26T03:50:34"},{"type":"QUALITY_GATE","status":"FAIL","score":0.925,"created_at":"2026-09-26T03:50:34"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T03:51:32"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:51:32"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:52:17"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:52:17"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:52:17"}],"detail_url":"/questions/24758","edit_url":"/questions/24758/edit","json_url":"/api/questions/24758","recheck_url":"/api/questions/24758/recheck"},{"id":24753,"job_id":3,"qa_status":"QUARANTINED","question_type":"fill_blank","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案1300.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"如图，\\(\\angle ABC = 30^{\\circ}\\)，点\\(O\\)为射线\\(BC\\)上一点，\\(BO = 8\\)，如果\\(\\odot O\\)是以点\\(O\\)为圆心，半径为$3 的圆，那么\\(odot O\\)与直线\\(BA\\)的位置关系是( ) .相离.相切.相交.不能确定","options":[],"answer":"","solution":"作\\(OD\\bot AB\\)于点\\(D\\),\\because\\(\\angle\\)ABC=30^{\\(\\circ\\)},BO=8\\(,\\therefore OD=\\frac{1}{2}OB=4,\\because \\odot O\\)的半径为3,4&gt;3,\\therefore \\odot O与直线BA$的位置关系是相离.故选A.","stem_html":"<div>如图，\\(\\angle ABC = 30^{\\circ}\\)，点\\(O\\)为射线\\(BC\\)上一点，\\(BO = 8\\)，如果\\(\\odot O\\)是以点\\(O\\)为圆心，半径为$3<span class=\"formula-fallback\">的圆，那么\\(odot O\\)与直线\\(BA\\)的位置关系是( ) .相离.相切.相交.不能确定</span><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/60e9949a-72b6-42a3-a206-822ed1d18d97/0cb2a5b52f8e.png\" style=\"width:123.5px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/2b06312b-7e3f-494e-ae3e-21d10207fcf7/60e9949a-72b6-42a3-a206-822ed1d18d97/b7a71b415b44.png\" style=\"width:134.7px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"></div>","answer_html":"","solution_html":"作\\(OD\\bot AB\\)于点\\(D\\),\\because\\(\\angle\\)ABC=30^{\\(\\circ\\)},BO=8\\(,\\therefore OD=\\frac{1}{2}OB=4,\\because \\odot O\\)的半径为3,4&gt;3,\\therefore \\odot O与直线BA$的位置关系是相离.故选A.","answer_missing":true,"formula_fallback":true,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T03:46:04"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:46:04"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:46:04"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T03:46:30"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T03:47:17"},{"type":"CRITIC","status":"FAIL","score":1.0,"created_at":"2026-09-26T03:47:17"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T03:47:17"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T03:48:17"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T03:48:17"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T03:49:00"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:49:00"},{"type":"COHERENCE","status":"PASS","score":0.95,"created_at":"2026-09-26T03:50:29"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:50:29"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.95,"created_at":"2026-09-26T03:50:29"}],"detail_url":"/questions/24753","edit_url":"/questions/24753/edit","json_url":"/api/questions/24753","recheck_url":"/api/questions/24753/recheck"},{"id":24724,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.95,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案130.pdf","job_source":"人教版.zip","pages":[3,3],"stem":"【小试2】 用公式法解下列方程： （1）\\(5x^{2}\\)+ 2x −1 = 0； （2）\\(6y^{2}\\)+ 13y + 6 = 0； （3）\\(x^{2}\\)+ 6x + 2 = 0．","options":[],"answer":"(1)\\(x_{1}\\)= 5,\\(x_{2}\\)= 5；(2)\\(y_{1}\\)= − _{3},\\(y_{2}\\)= − _{2}；(3)\\(x_{1}\\)= −3 + √7，\\(x_{2}\\)=−3 −√7.","solution":"(1)\\(5x^{2}\\)+ 2x −1 = 0, ∵a = 5, b = 2, c = −1, ∴\\(\\Delta =b^{2}\\)−4ac = 4 +\\(4 \\times 5 \\times 1 = 24\\)&gt;0, ∴x = −2±√24 = 10 −1±√6 −1+√6 −1−√6; 5, ∴\\(x_{1}\\)= 5,\\(x_{2}\\)= 5 (2)\\(6y^{2}\\)+ 13y + 6 = 0, ∵a = 6, b = 13, c = 6, ∴\\(\\Delta =b^{2}\\)−4ac = 169 −\\(4 \\times 6 \\times 6=25\\)&gt; 0, ∴y = −13±√25 = 12 −13±5 2 3 12, ∴\\(y_{1}\\)= − _{3},\\(y_{2}\\)= − _{2}; (3)\\(x^{2}\\)+ 6x + 2 = 0, ∴a = 1, b = 6, c = 2, ∴\\(\\Delta =b^{2}\\)−4ac = 36 −\\(4 \\times 1 \\times 2=28\\)&gt; 0, ∴x = −6±√28 = −3 ± 2 √7, ∴\\(x_{1}\\)= −3 + √7,\\(x_{2}\\)= −3 −√7.","stem_html":"<div>【小试2】 用公式法解下列方程：<br>（1）\\(5x^{2}\\)+ 2x −1 = 0；<br>（2）\\(6y^{2}\\)+ 13y + 6 = 0；<br>（3）\\(x^{2}\\)+ 6x + 2 = 0．</div>","answer_html":"(1)\\(x_{1}\\)= 5,\\(x_{2}\\)= 5；(2)\\(y_{1}\\)= − _{3},\\(y_{2}\\)= − _{2}；(3)\\(x_{1}\\)= −3 + √7，\\(x_{2}\\)=−3 −√7.","solution_html":"(1)\\(5x^{2}\\)+ 2x −1 = 0, ∵a = 5, b = 2, c = −1, ∴\\(\\Delta =b^{2}\\)−4ac = 4 +\\(4 \\times 5 \\times 1 = 24\\)&gt;0, ∴x = −2±√24 = 10 −1±√6 −1+√6 −1−√6; 5, ∴\\(x_{1}\\)= 5,\\(x_{2}\\)= 5 (2)\\(6y^{2}\\)+ 13y + 6 = 0, ∵a = 6, b = 13, c = 6, ∴\\(\\Delta =b^{2}\\)−4ac = 169 −\\(4 \\times 6 \\times 6=25\\)&gt; 0, ∴y = −13±√25 = 12 −13±5 2 3 12, ∴\\(y_{1}\\)= − _{3},\\(y_{2}\\)= − _{2}; (3)\\(x^{2}\\)+ 6x + 2 = 0, ∴a = 1, b = 6, c = 2, ∴\\(\\Delta =b^{2}\\)−4ac = 36 −\\(4 \\times 1 \\times 2=28\\)&gt; 0, ∴x = −6±√28 = −3 ± 2 √7, ∴\\(x_{1}\\)= −3 + √7,\\(x_{2}\\)= −3 −√7.","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T03:35:57"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:35:57"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:35:57"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T03:36:26"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T03:36:50"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:36:50"},{"type":"SYMBOLIC","status":"WARN","score":0.55,"created_at":"2026-09-26T03:36:50"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T03:38:47"},{"type":"QUALITY_GATE","status":"FAIL","score":0.95,"created_at":"2026-09-26T03:38:47"},{"type":"SOLVER","status":"PASS","score":0.6,"created_at":"2026-09-26T03:40:34"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:40:34"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:41:24"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:41:24"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:41:24"}],"detail_url":"/questions/24724","edit_url":"/questions/24724/edit","json_url":"/api/questions/24724","recheck_url":"/api/questions/24724/recheck"},{"id":24730,"job_id":3,"qa_status":"QUARANTINED","question_type":"choice","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案130.pdf","job_source":"人教版.zip","pages":[5,5],"stem":"若关于x的一元二次方程\\(x^{2}+ \\sqrt{a}x + 1 = 0\\)有两个相等的实数根，则实数a的值是( ). A. \\(1 \\frac{(C)4}{(D)-4} 4\\) B. − 14","options":[{"label":"A","text":"1 \\frac{(C)4}{(D)-4} 4"},{"label":"B","text":"− 14"}],"answer":"","solution":"","stem_html":"<div>若关于x的一元二次方程\\(x^{2}+ \\sqrt{a}x + 1 = 0\\)有两个相等的实数根，则实数a的值是( ).<br>A. \\(1 \\frac{(C)4}{(D)-4} 4\\)<br>B. − 14</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T03:33:54"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:33:54"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:33:54"},{"type":"VISION","status":"PASS","score":0.95,"created_at":"2026-09-26T03:34:11"},{"type":"SOLVER","status":"PASS","score":1.0,"created_at":"2026-09-26T03:35:32"},{"type":"CRITIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:35:32"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T03:35:32"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:35:50"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T03:35:50"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T03:38:11"},{"type":"CRITIC","status":"FAIL","score":0.95,"created_at":"2026-09-26T03:38:11"},{"type":"COHERENCE","status":"PASS","score":1.0,"created_at":"2026-09-26T03:39:21"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:39:21"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":1.0,"created_at":"2026-09-26T03:39:21"}],"detail_url":"/questions/24730","edit_url":"/questions/24730/edit","json_url":"/api/questions/24730","recheck_url":"/api/questions/24730/recheck"},{"id":24727,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.912,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案130.pdf","job_source":"人教版.zip","pages":[4,4],"stem":"用公式法解方程： （1）\\(2x^{2}\\)−5x + 3 = 0； （2）−2x(x + 1) = 1； （3）y(y - 3) = 2 + y(1 - 3y).","options":[],"answer":"","solution":"","stem_html":"<div>用公式法解方程：<br>（1）\\(2x^{2}\\)−5x + 3 = 0；<br>（2）−2x(x + 1) = 1；<br>（3）y(y - 3) = 2 + y(1 - 3y).</div>","answer_html":"","solution_html":"","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T03:30:30"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:30:30"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:30:30"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T03:30:44"},{"type":"SOLVER","status":"PASS","score":0.9,"created_at":"2026-09-26T03:31:45"},{"type":"CRITIC","status":"PASS","score":0.95,"created_at":"2026-09-26T03:31:45"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T03:31:45"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:31:58"},{"type":"QUALITY_GATE","status":"FAIL","score":0.912,"created_at":"2026-09-26T03:31:58"},{"type":"SOLVER","status":"PASS","score":0.8,"created_at":"2026-09-26T03:35:18"},{"type":"CRITIC","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:35:18"},{"type":"COHERENCE","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:38:15"},{"type":"SYMBOLIC","status":"PASS","score":1.0,"created_at":"2026-09-26T03:38:15"},{"type":"AUTO_REPAIR_ATTEMPT","status":"FAIL","score":0.9,"created_at":"2026-09-26T03:38:15"}],"detail_url":"/questions/24727","edit_url":"/questions/24727/edit","json_url":"/api/questions/24727","recheck_url":"/api/questions/24727/recheck"},{"id":24723,"job_id":3,"qa_status":"QUARANTINED","question_type":"comprehensive","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":null,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案130.pdf","job_source":"人教版.zip","pages":[2,3],"stem":"用公式法解下列方程： （1）^\\({3}_{2}x^{2}\\)+ 4x −1 = 0； （2）\\(6x^{2}\\)−4 = 3x； （3）\\(3x^{2}\\)+ 6x −1 = 0．","options":[],"answer":"(1)\\(x_{1}\\)= 3,\\(x_{2}\\)= 3 (2)\\(x_{1}\\)= 12,\\(x_{2}\\)= 12\\(x_{1}\\)=−1 + _{3}√3,\\(x_{2}\\)= −1 − _{3}√3","solution":"(1)∵a = _{2}, b = 4, c = −1, ∴\\(b^{2}\\)−4ac =\\(4^{2}\\)−\\(4 \\times 3 3_{2}\\times (−1) = 22\\)&gt; 0，代入求根公式，得x = −4±√22 =\\(2\\times ^{3}_{2}\\)−4±√22，∴\\(x_{1}\\)= −4+√22,\\(x_{2}\\)=−4−√22； 3 3 3 (2)将方程化为一般形式，得\\(6x^{2}\\)−3x −4 = 0, ∴a = 6, b = −3, c = −4,故\\(b^{2}\\)−4ac = (−3)^{2}−\\(4 \\times 6 \\times (−4) = 105\\)&gt; 0，代入求根公式，得 x=3±√105 = 3±√105, ∴\\(x_{1}\\)= 3+√105,\\(x_{2}\\)= 3−√105;\\(2\\times 6 12 12 12\\)(3)∵a = 3, b = 6, c = −1，∴\\(b^{2}\\)−4ac =\\(6^{2}\\)−\\(4 \\times 3 \\times (−1) = 48\\)&gt; 0，代入求根公式, 得: x = −6±√48 =\\(2\\times 3\\)−3±2√3 2 2 ，∴\\(x_{1}\\)= −1 + _{3}√3,\\(x_{2}\\)= −1 − _{3}√3 3 −1+√6 −1−√6 2 3","stem_html":"<div>用公式法解下列方程：<br>（1）^\\({3}_{2}x^{2}\\)+ 4x −1 = 0；<br>（2）\\(6x^{2}\\)−4 = 3x；<br>（3）\\(3x^{2}\\)+ 6x −1 = 0．</div>","answer_html":"(1)\\(x_{1}\\)= 3,\\(x_{2}\\)= 3 (2)\\(x_{1}\\)= 12,\\(x_{2}\\)= 12\\(x_{1}\\)=−1 + _{3}√3,\\(x_{2}\\)= −1 − _{3}√3","solution_html":"(1)∵a = _{2}, b = 4, c = −1, ∴\\(b^{2}\\)−4ac =\\(4^{2}\\)−\\(4 \\times 3 3_{2}\\times (−1) = 22\\)&gt; 0，代入求根公式，得x = −4±√22 =\\(2\\times ^{3}_{2}\\)−4±√22，∴\\(x_{1}\\)= −4+√22,\\(x_{2}\\)=−4−√22； 3 3 3 (2)将方程化为一般形式，得\\(6x^{2}\\)−3x −4 = 0, ∴a = 6, b = −3, c = −4,故\\(b^{2}\\)−4ac = (−3)^{2}−\\(4 \\times 6 \\times (−4) = 105\\)&gt; 0，代入求根公式，得 x=3±√105 = 3±√105, ∴\\(x_{1}\\)= 3+√105,\\(x_{2}\\)= 3−√105;\\(2\\times 6 12 12 12\\)(3)∵a = 3, b = 6, c = −1，∴\\(b^{2}\\)−4ac =\\(6^{2}\\)−\\(4 \\times 3 \\times (−1) = 48\\)&gt; 0，代入求根公式, 得: x = −6±√48 =\\(2\\times 3\\)−3±2√3 2 2 ，∴\\(x_{1}\\)= −1 + _{3}√3,\\(x_{2}\\)= −1 − _{3}√3 3 −1+√6 −1−√6 2 3","answer_missing":false,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":0.9,"created_at":"2026-09-26T03:32:29"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:32:29"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:32:29"},{"type":"VISION","status":"WARN","score":0.2,"created_at":"2026-09-26T03:33:40"}],"detail_url":"/questions/24723","edit_url":"/questions/24723/edit","json_url":"/api/questions/24723","recheck_url":"/api/questions/24723/recheck"},{"id":24722,"job_id":3,"qa_status":"QUARANTINED","question_type":"subjective","difficulty":2,"subject_code":"math","grade_level":"JUNIOR","subject_stage":"数学·初中","final_score":0.938,"source_file":"人教版/九上/2026江苏九年级期中数学试卷+答案130.pdf","job_source":"人教版.zip","pages":[2,2],"stem":"用公式法解下列方程： −\\(3x^{2}\\)+ 5x + 2 = 0;\\(\\frac{(1)}{(2)}x^{2}\\)+10 =\\(2 \\sqrt{5}x．\\)","options":[],"answer":"","solution":"− 3 + x + 2 = 0先化为标准形式 :\\(\\frac{(1)}{3} \\frac{x^{2}}{x} \\frac{5}{2}x^{2}\\)− − = 0, = 3,b = −5,c = −\\(2 \\frac{5}{(5)^{2}} \\frac{a}{43(2)}\\)= − −− = 25 + 24 = 49, 5  7 x =,解得\\(x_{1}\\)= 2,\\(x_{2}\\)= −\\(\\frac{1}{3}\\). 6\\(x^{2}\\)+ =\\(2 \\sqrt{5}x\\)先化为标准形式 :\\(\\frac{(2)}{x^{2}} \\frac{10}{x}\\)−\\(2 \\sqrt{5} +10 = 0, =1,b =\\)−2 5,c =\\(\\frac{a}{4110} \\frac{10}{20}\\)= (25)^{2}− − = 20 − 40 = −  0 方程没有实数根.","stem_html":"<div>用公式法解下列方程： −\\(3x^{2}\\)+ 5x + 2 = 0;\\(\\frac{(1)}{(2)}x^{2}\\)+10 =\\(2 \\sqrt{5}x．\\)</div>","answer_html":"","solution_html":"− 3 + x + 2 = 0先化为标准形式 :\\(\\frac{(1)}{3} \\frac{x^{2}}{x} \\frac{5}{2}x^{2}\\)− − = 0, = 3,b = −5,c = −\\(2 \\frac{5}{(5)^{2}} \\frac{a}{43(2)}\\)= − −− = 25 + 24 = 49, 5  7 x =,解得\\(x_{1}\\)= 2,\\(x_{2}\\)= −\\(\\frac{1}{3}\\). 6\\(x^{2}\\)+ =\\(2 \\sqrt{5}x\\)先化为标准形式 :\\(\\frac{(2)}{x^{2}} \\frac{10}{x}\\)−\\(2 \\sqrt{5} +10 = 0, =1,b =\\)−2 5,c =\\(\\frac{a}{4110} \\frac{10}{20}\\)= (25)^{2}− − = 20 − 40 = −  0 方程没有实数根.","answer_missing":true,"formula_fallback":false,"knowledge_points":[],"audits":[{"type":"STRUCTURE","status":"PASS","score":1.0,"created_at":"2026-09-26T03:30:28"},{"type":"FORMULA","status":"PASS","score":1.0,"created_at":"2026-09-26T03:30:28"},{"type":"KNOWLEDGE","status":"WARN","score":0.0,"created_at":"2026-09-26T03:30:28"},{"type":"VISION","status":"PASS","score":0.9,"created_at":"2026-09-26T03:31:25"},{"type":"SOLVER","status":"PASS","score":0.85,"created_at":"2026-09-26T03:32:03"},{"type":"CRITIC","status":"PASS","score":0.9,"created_at":"2026-09-26T03:32:03"},{"type":"SYMBOLIC","status":"WARN","score":0.5,"created_at":"2026-09-26T03:32:03"},{"type":"COHERENCE","status":"FAIL","score":0.95,"created_at":"2026-09-26T03:36:00"},{"type":"QUALITY_GATE","status":"FAIL","score":0.938,"created_at":"2026-09-26T03:36:00"}],"detail_url":"/questions/24722","edit_url":"/questions/24722/edit","json_url":"/api/questions/24722","recheck_url":"/api/questions/24722/recheck"}]}