{"ok":true,"question":{"id":21098,"question_uuid":"b293be50-5048-484b-b124-6d69deebe89c","job_id":4,"source_file":"A中考/2026江苏中考期末数学试卷+答案830.pdf","source_page_start":5,"source_page_end":5,"source_bbox":"[31.56, 421.86, 557.04, 796.15]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"comprehensive","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"【小试2】 ⏜ 正方形 ABCD 内接于 ⊙O, P 为BC上的一点,连接 DP, CP． ⏜ 2026-06-22\", \"type\": \"text\"}, {\"kind\": \"embedded_image\", \"type\": \"figure\", \"width\": 708, \"height\": 571, \"sha256\": \"6ba126b479d134d7bf4dbb8e109e418cc3fe0097c24a6e81681ba35f8d992874\", \"caption\": \"\", \"asset_key\": \"math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/b293be50-5048-484b-b124-6d69deebe89c/6ba126b479d1.png\", \"public_url\": \"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/b293be50-5048-484b-b124-6d69deebe89c/6ba126b479d1.png\", \"source_bbox\": [31.5, 527.8699951171875, 173.1999969482422, 652.8499755859375], \"source_page\": 5}, {\"type\": \"subquestion\", \"index\": 1, \"blocks\": [{\"text\": \"求∠CPD的度数;\", \"type\": \"text\"}]}, {\"type\": \"subquestion\", \"index\": 2, \"blocks\": [{\"text\": \"若⊙O的半径为r, 则阴影部分面积是______;\", \"type\": \"text\"}]}, {\"type\": \"subquestion\", \"index\": 3, \"blocks\": [{\"text\": \"当点 P 为BC的中点时, CP 是 ⊙O 的内接正 n 边形的一边,则n = ________．\", \"type\": \"text\"}]}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"(1)45°; (2)\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"1_{4}\"}, {\"text\": \"(\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\pi\"}, {\"text\": \"−2)\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"r^{2}\"}, {\"text\": \"; (3)8.\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"(1)连接 OD, OC, ∵ 正方形 ABCD 内接于 ⊙O,所以∠DOC = 90°, ∠DPC=\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"1_{2}\"}, {\"text\": \"∠DOC = 45°.\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"90\\\\pi{}r2 1 1\"}, {\"text\": \"(2)S扇形_{COD} −S△COD= _{360}− _{2}\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"r^{2}\"}, {\"text\": \"= _{4}(\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\pi\"}, {\"text\": \"−2)\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"r^{2}\"}, {\"text\": \". ⏜ ⏜ ⏜ (3)连接 PO, OB, ∵ 正方形 ABCD 内接于 ⊙O, ∴∠COB = 90°, ∵ 点 P 为BC中点, ∴CP = BP, ∴∠COP =\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"1 _{2}\"}, {\"text\": \"∠COB = 45°, ∴n = 360 ÷ 45 = 8. 2026-06-22\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [31.56, 421.86, 557.04, 796.15], \"file\": \"A中考/2026江苏中考期末数学试卷+答案830.pdf\", \"regions\": [{\"bbox\": [31.56, 421.86, 557.04, 796.15], \"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, 501.27, 557.04, 796.15], \"page\": 10}]}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"2\", \"subject_code\": \"math\", \"question_type\": \"comprehensive\", \"content_sha256\": \"7334dbf2eeb8c487f290d7a1a240ab28494d4c042bc2a69eda512e449891a8f8\"}","body_html":"
【小试2】 ⏜ 正方形 ABCD 内接于 ⊙O, P 为BC上的一点,连接 DP, CP． ⏜ 2026-06-22\"\"
（1）求∠CPD的度数;
（2）若⊙O的半径为r, 则阴影部分面积是______;
（3）当点 P 为BC的中点时, CP 是 ⊙O 的内接正 n 边形的一边,则n = ________．
","answer_html":"(1)45°; (2)\\(1_{4}\\)(\\(\\pi\\)−2)\\(r^{2}\\); (3)8.","ways_html":"(1)连接 OD, OC, ∵ 正方形 ABCD 内接于 ⊙O,所以∠DOC = 90°, ∠DPC=\\(1_{2}\\)∠DOC = 45°.\\(90\\pi{}r2 1 1\\)(2)S扇形_{COD} −S△COD= _{360}− _{2}\\(r^{2}\\)= _{4}(\\(\\pi\\)−2)\\(r^{2}\\). ⏜ ⏜ ⏜ (3)连接 PO, OB, ∵ 正方形 ABCD 内接于 ⊙O, ∴∠COB = 90°, ∵ 点 P 为BC中点, ∴CP = BP, ∴∠COP =\\(1 _{2}\\)∠COB = 45°, ∴n = 360 ÷ 45 = 8. 2026-06-22","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=8092): Read timed out. (read timeout=120) [endpoints: http://127.0.0.1:8091/v1 -> http://127.0.0.1:8092/v1]","published_question_id":null,"content_sha256":"7334dbf2eeb8c487f290d7a1a240ab28494d4c042bc2a69eda512e449891a8f8","created_at":"2026-09-24T22:35:08","updated_at":"2026-09-24T22:46:42","answer_missing":false,"formula_fallback":false,"_number":"2","_section":"quiz","_section_label":"小试牛刀 ★ 独立完成，见证实力！"},"assets":[{"id":4605,"asset_uuid":"e1ae09effd7c408abec7be60fc8908d6","job_id":4,"import_question_id":21098,"asset_type":"embedded_image","source_file":"2026江苏中考期末数学试卷+答案830.pdf","source_page":5,"source_bbox":"[31.5, 527.87, 173.2, 652.85]","sha256":"6ba126b479d134d7bf4dbb8e109e418cc3fe0097c24a6e81681ba35f8d992874","local_path":"/www/wwwroot/tikupdfpng.mtwlkj.net_5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/b293be50-5048-484b-b124-6d69deebe89c/6ba126b479d1.png","asset_key":"math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/b293be50-5048-484b-b124-6d69deebe89c/6ba126b479d1.png","public_url":"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/b293be50-5048-484b-b124-6d69deebe89c/6ba126b479d1.png","width":708,"height":571,"qa_status":"PENDING","created_at":"2026-09-24T22:36:59","safe_public_url":"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/b293be50-5048-484b-b124-6d69deebe89c/6ba126b479d1.png"}],"knowledge":[],"audits":[{"id":415145,"import_question_id":21098,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"【小试2】 ⏜ 正方形 ABCD 内接于 ⊙O, P 为BC上的一点,连接 DP, CP． ⏜ 2026-06-22 [图] (1) 求∠CPD的度数; (2) 若⊙O的半径为r, 则阴影部分面积是______; (3) 当点 P 为BC的中点时, CP 是 ⊙O 的内接正 n 边形的一边,则n = ________．","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-24T22:42:42"},{"id":415146,"import_question_id":21098,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"1_{4}; \\pi; r^{2}; 1_{2}; 90\\pi{}r2 1 1","result_json":"{\"risky\": 6, \"issues\": [], \"checked\": 9, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-24T22:42:42"},{"id":415147,"import_question_id":21098,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"【小试2】 ⏜ 正方形 ABCD 内接于 ⊙O, P 为BC上的一点,连接 DP, CP． ⏜ 2026-06-22 [图] (1) 求∠CPD的度数; (2) 若⊙O的半径为r, 则阴影部分面积是______; (3) 当点 P 为BC的中点时, CP 是 ⊙O 的内接正 n 边形的一边,则n = ________．","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-24T22:42:42"},{"id":415152,"import_question_id":21098,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.95,"input_snapshot":"题干：\n【小试2】 ⏜ 正方形 ABCD 内接于 ⊙O, P 为BC上的一点,连接 DP, CP． ⏜ 2026-06-22 （1）求∠CPD的度数; （2）若⊙O的半径为r, 则阴影部分面积是______; （3）当点 P 为BC的中点时, CP 是 ⊙O 的内接正 n 边形的一边,则n = ________．\n答案：\n(1)45°; (2)\\(1_{4}\\)(\\(\\pi\\)−2)\\(r^{2}\\); (3)8.\n解析：\n(1)连接 OD, OC, ∵ 正方形 ABCD 内接于 ⊙O,所以∠DOC = 90°, ∠DPC=\\(1_{2}\\)∠DOC = 45°.\\(90\\pi{}r2 1 1\\)(2)S扇形_{COD} −S△COD= _{360}− _{2}\\(r^{2}\\)= _{4}(\\(\\pi\\)−2)\\(r^{2}\\). ⏜ ⏜ ⏜ (3)连接 PO, OB, ∵ 正方形 ABCD 内接于 ⊙O, ∴∠COB = 90°, ∵ 点 P 为BC中点, ∴CP = BP, ∴∠COP =\\(1 _{2}\\)∠COB = 45°, ∴n = 360 ÷ 45 = 8. 2026-06-22","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.95, \"suggestions\": [\"解析中公式排版较乱，建议优化为更清晰的数学表达式格式\"]}","created_at":"2026-09-24T22:43:19"}]}