{"ok":true,"question":{"id":21052,"question_uuid":"0a77f7f4-64c0-4773-b5d4-00a058c5e64d","job_id":4,"source_file":"A中考/2026江苏中考期末数学试卷+答案825.pdf","source_page_start":5,"source_page_end":5,"source_bbox":"[31.56, 157.09, 393.13, 234.88]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"comprehensive","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"【小试1】 如图,⊙O是△ABC的外接圆, AB是⊙O的直径, ∠BAC的平分线交⊙ O于点D, 过点D作BC的平行线交AC的延长线于点E.\", \"type\": \"text\"}, {\"kind\": \"embedded_image\", \"type\": \"figure\", \"width\": 708, \"height\": 604, \"sha256\": \"58a89d99e66df762bfc8c2a999030a0d5c31503b41fa22dd421687fb3b674ba8\", \"caption\": \"\", \"asset_key\": \"math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/0a77f7f4-64c0-4773-b5d4-00a058c5e64d/58a89d99e66d.png\", \"public_url\": \"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/0a77f7f4-64c0-4773-b5d4-00a058c5e64d/58a89d99e66d.png\", \"source_bbox\": [31.5, 235.24996948242188, 173.1999969482422, 367.7799682617187], \"source_page\": 5}, {\"type\": \"subquestion\", \"index\": 1, \"blocks\": [{\"text\": \"求证: DE是⊙O的切线;\", \"type\": \"text\"}]}, {\"type\": \"subquestion\", \"index\": 2, \"blocks\": [{\"text\": \"若∠BAC = 60∘, CE = √3, 求⊙O的半径.\", \"type\": \"text\"}]}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"(1)见解析; (2)\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"2\\\\sqrt{3}\"}, {\"text\": \"．\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"(1)连接OD,⊙O是△ABC的外接圆, AB是⊙O的直径, ∴∠ACB = 90∘,OA= OD, ∴∠OAD = ∠ODA, ∵ DE ∥BC, ∴∠AED = ∠ACB = 90∘,∵∠BAC的平分线交⊙O于点D, ∴∠EAD = ∠BAD, ∴∠EAD =∠ADO,∴ OD ∥AE, ∴∠ODE = 180∘−∠AED = 90∘, ∵OD为⊙O的半径, ∴DE是⊙O的切线; (2)设OD交BC于点F, ∵∠BAC = 60∘, ∠ACB = 90∘,∴∠ABC = 30∘, ∵CE ∥DF, DE ∥CF, ∠E = 90∘, ∴ 四边形CEDF为矩形,∴∠DFC = 90∘, DF = CE = √3, ∴∠OFB = 90∘, 设⊙O的半径为r, 则:OB= OD = r, OF = OD −DF = r −√3, ∵∠OFB = 90∘, ∠ABC = 30∘, ∴OB =2OF,∴r = 2(r −√3), ∴r = 2√3, ∴⊙ O的半径为2√3．\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [31.56, 157.09, 393.13, 234.88], \"file\": \"A中考/2026江苏中考期末数学试卷+答案825.pdf\", \"regions\": [{\"bbox\": [31.56, 157.09, 393.13, 234.88], \"page\": 5}], \"section\": \"quiz\", \"page_end\": 5, \"page_start\": 5, \"section_label\": \"小试牛刀   ★ 独立完成，见证实力！\", \"answer_regions\": [{\"bbox\": [30.0, 177.75, 552.88, 363.31], \"page\": 10}]}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"1\", \"subject_code\": \"math\", \"question_type\": \"comprehensive\", \"content_sha256\": \"438564ddaa2e95eaa3d60343d7e39a197472032a26fe171a3df8df74bada7f22\"}","body_html":"<div>【小试1】 如图,⊙O是△ABC的外接圆, AB是⊙O的直径, ∠BAC的平分线交⊙ O于点D, 过点D作BC的平行线交AC的延长线于点E.<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/0a77f7f4-64c0-4773-b5d4-00a058c5e64d/58a89d99e66d.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）求证: DE是⊙O的切线;<br>（2）若∠BAC = 60∘, CE = √3, 求⊙O的半径.</div>","answer_html":"(1)见解析; (2)\\(2\\sqrt{3}\\)．","ways_html":"(1)连接OD,⊙O是△ABC的外接圆, AB是⊙O的直径, ∴∠ACB = 90∘,OA= OD, ∴∠OAD = ∠ODA, ∵ DE ∥BC, ∴∠AED = ∠ACB = 90∘,∵∠BAC的平分线交⊙O于点D, ∴∠EAD = ∠BAD, ∴∠EAD =∠ADO,∴ OD ∥AE, ∴∠ODE = 180∘−∠AED = 90∘, ∵OD为⊙O的半径, ∴DE是⊙O的切线; (2)设OD交BC于点F, ∵∠BAC = 60∘, ∠ACB = 90∘,∴∠ABC = 30∘, ∵CE ∥DF, DE ∥CF, ∠E = 90∘, ∴ 四边形CEDF为矩形,∴∠DFC = 90∘, DF = CE = √3, ∴∠OFB = 90∘, 设⊙O的半径为r, 则:OB= OD = r, OF = OD −DF = r −√3, ∵∠OFB = 90∘, ∠ABC = 30∘, ∴OB =2OF,∴r = 2(r −√3), ∴r = 2√3, ∴⊙ O的半径为2√3．","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":null,"error_message":"处理异常: LLM call failed after retries: HTTPConnectionPool(host='127.0.0.1', port=8091): Read timed out. (read timeout=120) [endpoints: http://127.0.0.1:8092/v1 -> http://127.0.0.1:8091/v1]","published_question_id":null,"content_sha256":"438564ddaa2e95eaa3d60343d7e39a197472032a26fe171a3df8df74bada7f22","created_at":"2026-09-24T22:16:34","updated_at":"2026-09-24T22:25:14","answer_missing":false,"formula_fallback":false,"_number":"1","_section":"quiz","_section_label":"小试牛刀   ★ 独立完成，见证实力！"},"assets":[{"id":4592,"asset_uuid":"26b84ebaadbe4ba3ae9241a5ec7ac7b1","job_id":4,"import_question_id":21052,"asset_type":"embedded_image","source_file":"2026江苏中考期末数学试卷+答案825.pdf","source_page":5,"source_bbox":"[31.5, 235.25, 173.2, 367.78]","sha256":"58a89d99e66df762bfc8c2a999030a0d5c31503b41fa22dd421687fb3b674ba8","local_path":"/www/wwwroot/tikupdfpng.mtwlkj.net_5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/0a77f7f4-64c0-4773-b5d4-00a058c5e64d/58a89d99e66d.png","asset_key":"math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/0a77f7f4-64c0-4773-b5d4-00a058c5e64d/58a89d99e66d.png","public_url":"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/0a77f7f4-64c0-4773-b5d4-00a058c5e64d/58a89d99e66d.png","width":708,"height":604,"qa_status":"PENDING","created_at":"2026-09-24T22:16:34","safe_public_url":"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/0a77f7f4-64c0-4773-b5d4-00a058c5e64d/58a89d99e66d.png"}],"knowledge":[],"audits":[{"id":414407,"import_question_id":21052,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"【小试1】 如图,⊙O是△ABC的外接圆, AB是⊙O的直径, ∠BAC的平分线交⊙ O于点D, 过点D作BC的平行线交AC的延长线于点E. [图] (1) 求证: DE是⊙O的切线; (2) 若∠BAC = 60∘, CE = √3, 求⊙O的半径.","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-24T22:21:14"},{"id":414408,"import_question_id":21052,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"2\\sqrt{3}","result_json":"{\"risky\": 1, \"issues\": [], \"checked\": 1, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-24T22:21:14"},{"id":414409,"import_question_id":21052,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"【小试1】 如图,⊙O是△ABC的外接圆, AB是⊙O的直径, ∠BAC的平分线交⊙ O于点D, 过点D作BC的平行线交AC的延长线于点E. [图] (1) 求证: DE是⊙O的切线; (2) 若∠BAC = 60∘, CE = √3, 求⊙O的半径.","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-24T22:21:14"},{"id":414433,"import_question_id":21052,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":1.0,"input_snapshot":"题干：\n【小试1】 如图,⊙O是△ABC的外接圆, AB是⊙O的直径, ∠BAC的平分线交⊙ O于点D, 过点D作BC的平行线交AC的延长线于点E. （1）求证: DE是⊙O的切线; （2）若∠BAC = 60∘, CE = √3, 求⊙O的半径.\n答案：\n(1)见解析; (2)\\(2\\sqrt{3}\\)．\n解析：\n(1)连接OD,⊙O是△ABC的外接圆, AB是⊙O的直径, ∴∠ACB = 90∘,OA= OD, ∴∠OAD = ∠ODA, ∵ DE ∥BC, ∴∠AED = ∠ACB = 90∘,∵∠BAC的平分线交⊙O于点D, ∴∠EAD = ∠BAD, ∴∠EAD =∠ADO,∴ OD ∥AE, ∴∠ODE = 180∘−∠AED = 90∘, ∵OD为⊙O的半径, ∴DE是⊙O的切线; (2)设OD交BC于点F, ∵∠BAC = 60∘, ∠ACB = 90∘,∴∠ABC = 30∘, ∵CE ∥DF, DE ∥CF, ∠E = 90∘, ∴ 四边形CEDF为矩形,∴∠DFC = 90∘, DF = CE = √3, ∴∠OFB = 90∘, 设⊙O的半径为r, 则:OB= OD = r, OF = OD −DF = r −√3, ∵∠OFB = 90∘, ∠ABC = 30∘, ∴OB =2OF,∴r = 2(r −√3), ∴r = 2√3, ∴⊙ O的半径为2√3．","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 1.0, \"suggestions\": [\"解析中‘CE ∥ DF’的表述可优化为‘由矩形CEDF性质可知CE ∥ DF’，以增强逻辑连贯性\"]}","created_at":"2026-09-24T22:21:52"}]}