{"ok":true,"question":{"id":21053,"question_uuid":"04d71393-bf34-450a-8dca-fc6b1d528de8","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, 479.58, 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】 如图,⊙O的半径为4cm, 其内接正六边形ABCDEF, 点P, Q同 时分别从A, D两点出发, 以1cm/s的速度沿AF, DC向终点F, C运动, 连接PB, QE, PE, BQ. 设运动时间为t(s). 2026-06-22\", \"type\": \"text\"}, {\"kind\": \"embedded_image\", \"type\": \"figure\", \"width\": 708, \"height\": 595, \"sha256\": \"6a9823c55a03e569eaea6ea46ba277e7cc9a27d02961cc51450d78c25e2e5bc7\", \"caption\": \"\", \"asset_key\": \"math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/04d71393-bf34-450a-8dca-fc6b1d528de8/6a9823c55a03.png\", \"public_url\": \"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/04d71393-bf34-450a-8dca-fc6b1d528de8/6a9823c55a03.png\", \"source_bbox\": [31.5, 602.1400146484375, 173.1999969482422, 732.0599975585938], \"source_page\": 5}, {\"type\": \"subquestion\", \"index\": 1, \"blocks\": [{\"text\": \"求证: 四边形PBQE为平行四边形;\", \"type\": \"text\"}]}, {\"type\": \"subquestion\", \"index\": 2, \"blocks\": [{\"text\": \"填空: ①当t = ____s时, 四边形PBQE为菱形; ②当t = ______s时, 四边形PBQE为矩形．\", \"type\": \"text\"}]}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"(1)见解析; (2)①2; ②0或4．\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"(1)∵正六边形ABCDEF内接于⊙O, ∴AB = BC = CD = DE = EF =FA,∠A = ∠ABC = ∠C = ∠D = ∠DEF = ∠F. ∵点P, Q同时分别从A, D两点出发, 以1cm/s的速度沿AF, DC向终点F, C运动, ∴AP = AB = DE DQ = t,PF= QC = 4 −t.在 △ABP 和 △DEQ 中， ∵{∠A = ∠D, ∴△ABP ≅△DEQ(SAS).∴BP = EQ. AP = DQ 同理可证PE = QB，∴四边形PBQE是平行四边形． (2)①当PA = PF, QC = QD时, 四边形PBQE是菱形, 此时t = 2. ②当t = 0时,∠EPF = ∠PEF = 30∘, ∴ 2026-06-22 ∠BPE = 120∘−30∘= 90∘. ∴此时四边形PBQE是矩形. 当t = 4时, 同理可知∠BPE = 90∘, 此时四边形PBQE是矩形.综上所述, 当t = 0或4时, 四边形PBQE是矩形. 故答案为:①2; ②0或4．\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [31.56, 479.58, 557.04, 796.15], \"file\": \"A中考/2026江苏中考期末数学试卷+答案825.pdf\", \"regions\": [{\"bbox\": [31.56, 479.58, 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, 598.67, 557.04, 796.15], \"page\": 10}, {\"bbox\": [30.0, 129.1, 558.0, 174.4], \"page\": 11}]}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"2\", \"subject_code\": \"math\", \"question_type\": \"comprehensive\", \"content_sha256\": \"0f96ce2c221d2d2c28c90ea3a4e93fb5a338333252a19b853e1e890b4db64fdc\"}","body_html":"<div>【小试2】 如图,⊙O的半径为4cm, 其内接正六边形ABCDEF, 点P, Q同 时分别从A, D两点出发, 以1cm/s的速度沿AF, DC向终点F, C运动, 连接PB, QE, PE, BQ. 设运动时间为t(s). 2026-06-22<img class=\"question-figure\" src=\"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/04d71393-bf34-450a-8dca-fc6b1d528de8/6a9823c55a03.png\" style=\"width:188.9px!important;max-width:100%;height:auto\" alt=\"\" title=\"点击查看原图\"><br>（1）求证: 四边形PBQE为平行四边形;<br>（2）填空: ①当t = ____s时, 四边形PBQE为菱形; ②当t = ______s时, 四边形PBQE为矩形．</div>","answer_html":"(1)见解析; (2)①2; ②0或4．","ways_html":"(1)∵正六边形ABCDEF内接于⊙O, ∴AB = BC = CD = DE = EF =FA,∠A = ∠ABC = ∠C = ∠D = ∠DEF = ∠F. ∵点P, Q同时分别从A, D两点出发, 以1cm/s的速度沿AF, DC向终点F, C运动, ∴AP = AB = DE DQ = t,PF= QC = 4 −t.在 △ABP 和 △DEQ 中， ∵{∠A = ∠D, ∴△ABP ≅△DEQ(SAS).∴BP = EQ. AP = DQ 同理可证PE = QB，∴四边形PBQE是平行四边形． (2)①当PA = PF, QC = QD时, 四边形PBQE是菱形, 此时t = 2. ②当t = 0时,∠EPF = ∠PEF = 30∘, ∴ 2026-06-22 ∠BPE = 120∘−30∘= 90∘. ∴此时四边形PBQE是矩形. 当t = 4时, 同理可知∠BPE = 90∘, 此时四边形PBQE是矩形.综上所述, 当t = 0或4时, 四边形PBQE是矩形. 故答案为:①2; ②0或4．","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":"0f96ce2c221d2d2c28c90ea3a4e93fb5a338333252a19b853e1e890b4db64fdc","created_at":"2026-09-24T22:16:34","updated_at":"2026-09-24T22:25:50","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":4594,"asset_uuid":"91100d7818834fdb8acea5239b1a4022","job_id":4,"import_question_id":21053,"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, 602.14, 173.2, 732.06]","sha256":"6a9823c55a03e569eaea6ea46ba277e7cc9a27d02961cc51450d78c25e2e5bc7","local_path":"/www/wwwroot/tikupdfpng.mtwlkj.net_5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/04d71393-bf34-450a-8dca-fc6b1d528de8/6a9823c55a03.png","asset_key":"math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/04d71393-bf34-450a-8dca-fc6b1d528de8/6a9823c55a03.png","public_url":"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/04d71393-bf34-450a-8dca-fc6b1d528de8/6a9823c55a03.png","width":708,"height":595,"qa_status":"PENDING","created_at":"2026-09-24T22:17:49","safe_public_url":"http://tikupdfpng.mtwlkj.net:5129/qbank/math/2026/09/16de2e24-a616-456b-83c5-3364ab6bd928/04d71393-bf34-450a-8dca-fc6b1d528de8/6a9823c55a03.png"}],"knowledge":[],"audits":[{"id":414426,"import_question_id":21053,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"【小试2】 如图,⊙O的半径为4cm, 其内接正六边形ABCDEF, 点P, Q同 时分别从A, D两点出发, 以1cm/s的速度沿AF, DC向终点F, C运动, 连接PB, QE, PE, BQ. 设运动时间为t(s). 2026-06-22 [图] (1) 求证: 四边形PBQE为平行四边形; (2) 填空: ①当t = ____s时, 四边形PBQE为菱形; ②当t = ______s时, 四边形PBQE为矩形．","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-24T22:21:50"},{"id":414427,"import_question_id":21053,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"","result_json":"{\"note\": \"无公式块\", \"checked\": 0}","created_at":"2026-09-24T22:21:50"},{"id":414428,"import_question_id":21053,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"【小试2】 如图,⊙O的半径为4cm, 其内接正六边形ABCDEF, 点P, Q同 时分别从A, D两点出发, 以1cm/s的速度沿AF, DC向终点F, C运动, 连接PB, QE, PE, BQ. 设运动时间为t(s). 2026-06-22 [图] (1) 求证: 四边形PBQE为平行四边形; (2) 填空: ①当t = ____s时, 四边形PBQE为菱形; ②当t = ______s时, 四边形PBQE为矩形．","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-24T22:21:50"},{"id":414492,"import_question_id":21053,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.95,"input_snapshot":"题干：\n【小试2】 如图,⊙O的半径为4cm, 其内接正六边形ABCDEF, 点P, Q同 时分别从A, D两点出发, 以1cm/s的速度沿AF, DC向终点F, C运动, 连接PB, QE, PE, BQ. 设运动时间为t(s). 2026-06-22 （1）求证: 四边形PBQE为平行四边形; （2）填空: ①当t = ____s时, 四边形PBQE为菱形; ②当t = ______s时, 四边形PBQE为矩形．\n答案：\n(1)见解析; (2)①2; ②0或4．\n解析：\n(1)∵正六边形ABCDEF内接于⊙O, ∴AB = BC = CD = DE = EF =FA,∠A = ∠ABC = ∠C = ∠D = ∠DEF = ∠F. ∵点P, Q同时分别从A, D两点出发, 以1cm/s的速度沿AF, DC向终点F, C运动, ∴AP = AB = DE DQ = t,PF= QC = 4 −t.在 △ABP 和 △DEQ 中， ∵{∠A = ∠D, ∴△ABP ≅△DEQ(SAS).∴BP = EQ. AP = DQ 同理可证PE = QB，∴四边形PBQE是平行四边形． (2)①当PA = PF, QC = QD时, 四边形PBQE是菱形, 此时t = 2. ②当t = 0时,∠EPF = ∠PEF = 30∘, ∴ 2026-06-22 ∠BPE = 120∘−30∘= 90∘. ∴此时四边形PBQE是矩形. 当t = 4时, 同理可知∠BPE = 90∘, 此时四边形PBQE是矩形.综上所述, 当t = 0或4时, 四边形PBQE是矩形. 故答案为:①2; ②0或4．","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.95, \"suggestions\": [\"解析中“AP = AB = DE DQ = t”存在排版歧义，建议明确为“AP = DQ = t”并单独说明AB=DE的推导依据\"]}","created_at":"2026-09-24T22:25:21"}]}