真题
1 . 如图,EP交圆于E、C两点,PD切圆于D,G为CE上一点且
,连接DG并延长交圆于点A,作弦AB垂直EP,垂足为F.
(1)求证:AB为圆的直径;
(2)若AC=BD,求证:AB=ED.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a3450abdd309e47cd7c33085d68ee.png)
(1)求证:AB为圆的直径;
(2)若AC=BD,求证:AB=ED.
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571783841030144/1571783846731776/STEM/29d6e840-e7ac-492a-8734-63aeab4097ca.png)
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云南省保山第九中学2021届高三上学期阶段测试文科数学试题2014年全国普通高等学校招生统一考试理科数学(辽宁卷)2014年全国普通高等学校招生统一考试文科数学(辽宁卷)(已下线)2013-2014学年黑龙江省鹤岗一中高二下学期期末考试理科数学试卷2016届吉林省实验中学高三上学期二模理科数学试卷福建省2016届高三毕业班总复习(几何选讲)单元过关形成性测试卷(文理科)数学试题
9-10高二下·海南·期末
真题
名校
2 . 如图,已知AP是⊙O的切线,P为切点,AC是⊙O的割线,与⊙O交于B、C两点,圆心O在
的内部,点M是BC的中点.
![](https://img.xkw.com/dksih/QBM/2010/8/13/1569813231534080/1569813236572160/STEM/b6f90bfca2dc491d8eb11c5269ac68ae.png?resizew=168)
(1)证明A,P,O,M四点共圆;
(2)求∠OAM+∠APM的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32986401a4d24904d5e446fa9210ac6.png)
![](https://img.xkw.com/dksih/QBM/2010/8/13/1569813231534080/1569813236572160/STEM/b6f90bfca2dc491d8eb11c5269ac68ae.png?resizew=168)
(1)证明A,P,O,M四点共圆;
(2)求∠OAM+∠APM的大小.
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14卷引用:2012届云南省昆明八中高三上学期理科数学期中考试试卷
(已下线)2012届云南省昆明八中高三上学期理科数学期中考试试卷(已下线)2010年海南省嘉积中学高二下学期期末测试数学文2007年普通高等学校招生全国统一考试理科数学卷(海南)(已下线)2011届河南省开封市高三统考理科数学卷(已下线)2011届海南省嘉积中学高三上学期第二次月考文科数学卷(已下线)2013届辽宁沈阳二中等重点中学协作体高三领航高考预测(八)文数学卷2017届河北省五个一名校联盟高三上学期一模数学(文)试卷2017届甘肃会宁县一中高三上学期9月月考数学(理)试卷2017届甘肃会宁县一中高三上学期9月月考数学(文)试卷2017届河北省五个一联盟(石家庄一中、保定一中等)高三上学期第一次模拟考试数学(文)试卷2017年江西省“北阳四校”高三开学摸底考试数学(文科)福建省永春一中、培元中学、季延中学、石光中学2017届高三第一次联合考试数学(理)试题2007年普通高等学校招生考试数学(文)试题(琼、宁卷)2007年普通高等学校招生考试数学(理)试题(琼、宁卷)
3 . 如图,已知
是
中
边上的高,以
为直径的
分别交
、
于点
、
,点
是
的中点.
.
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572587514535936/1572587520811008/STEM/484a4ff298fa40148dd274ba3b2ea624.png)
(1)求证:
是
的切线;
(2)求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572587514535936/1572587520811008/STEM/05408a25b4b24591a105b31ce1f050b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f3956f008cc29ca4bae44a087d5427.png)
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572587514535936/1572587520811008/STEM/4a8063f6be2142b3a68f4d8e067cad24.png)
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572587514535936/1572587520811008/STEM/484a4ff298fa40148dd274ba3b2ea624.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572587514535936/1572587520811008/STEM/cf3b73a035634bf6a2aec0719e339f8c.png)
(2)求
![](https://img.xkw.com/dksih/QBM/2016/4/8/1572587514535936/1572587520811008/STEM/b060012edc4b4489a1327c801ce2121f.png)
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4 . 如图,
是⊙
的直径,
与⊙
相切于
是⊙
的弦,
是
弧的中点,
的延长线与
交于
.
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572577405771776/1572577411751936/STEM/143e4b78a1af4c758a9492913fd5eabc.png?resizew=253)
(1)求证:
;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b368aa0a9bd8d05172d13f7718afbcbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2016/4/7/1572577405771776/1572577411751936/STEM/143e4b78a1af4c758a9492913fd5eabc.png?resizew=253)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c92206888f6d17cd3b0bd05d38113e3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15d29f2f3c2ff7c3b7016500461859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2卷引用:2016届云南省高三下学期第一次高中毕业生复习统一测试理科数学试卷
5 . 如图,
交圆于
两点,
切圆于
为
上一点,且
,连接
并延长交圆于点
,作弦
垂直
垂足为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/8b05457f-a85b-413e-8324-3b195a27aa59.png?resizew=230)
(1)求证:
为圆的直径;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8fe5165aee9f67db70b508b6fbaf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d307b3c4da63535e665ce0a17712eb47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a3450abdd309e47cd7c33085d68ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/8b05457f-a85b-413e-8324-3b195a27aa59.png?resizew=230)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06cd62abe5e301e96111b5060d0c456c.png)
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14-15高三上·河南·期中
名校
6 . 选修4-1:几何证明选讲
如图,四边形ABCD是⊙O的内接四边形,AB的延长线与DC的延长线交于点E,且CB=CE.
![](https://img.xkw.com/dksih/QBM/2014/12/18/1571927585906688/1571927591313408/STEM/e4de028d4f8e4007b9f6c0ab06599d52.png)
(1)证明:∠D=∠E;
(2)设AD不是⊙O的直径,AD的中点为M,且MB=MC,证明:△ADE为等边三角形.
如图,四边形ABCD是⊙O的内接四边形,AB的延长线与DC的延长线交于点E,且CB=CE.
![](https://img.xkw.com/dksih/QBM/2014/12/18/1571927585906688/1571927591313408/STEM/e4de028d4f8e4007b9f6c0ab06599d52.png)
(1)证明:∠D=∠E;
(2)设AD不是⊙O的直径,AD的中点为M,且MB=MC,证明:△ADE为等边三角形.
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2014·吉林·模拟预测
7 . 【选修4-1:几何证明选讲】
如图,
为直角三角形,
,以AB为直径的圆交AC于点E,点D是BC边的中点,连接OD交圆O于点M,求证:
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571962711490560/1571962841948160/STEM/00737b15f870441ebd599c646e311425.png)
(Ⅰ)O、B、D、E四点共圆;
(Ⅱ)
.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c38d26d85081a99d51e2f686817e94.png)
![](https://img.xkw.com/dksih/QBM/2015/1/14/1571962711490560/1571962841948160/STEM/00737b15f870441ebd599c646e311425.png)
(Ⅰ)O、B、D、E四点共圆;
(Ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7332ae405de6267bd0b704afae772f5c.png)
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2015届云南省师大附中高三高考适应性月考理科数学试卷2015届云南省师大附中高三高考适应性月考文科数学试卷(已下线)2015届吉林省实验中学高三第四次模拟考试理科数学试卷2014-2015学年湖北省宜昌市高二下学期期末文科数学试卷
2012·河南焦作·一模
8 . 在
中,AB=AC,过点A的直线与其外接圆交于点P,交BC延长线于点D.
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/13cf603650fe4de19d4d0d65cea4b9fc.png)
(1)求证:
;
(2)若AC=3,求
的值.
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/4068bd6d669d4586b69702cb3762e8c2.png)
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/13cf603650fe4de19d4d0d65cea4b9fc.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/0a245338e40a4c728e67305b45866c4f.png)
(2)若AC=3,求
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/3d841a1467fa49a59809ed6a011bc517.png)
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(已下线)2014届云南部分名校(玉溪一中)高三11月月考理科数学试卷(已下线)2012届河南省焦作市高三第一次质量检测理科数学试卷(已下线)2012届河南省焦作市高三第一次质量检测文科数学试卷(已下线)2012届黑龙江省哈六中高三第三次模拟考试理科数学试卷(已下线)2012届河北省唐山一中高三第一次高考仿真测试理科数学试卷(已下线)2013届甘肃省河西五市部分普通高中高三第二次(5月)联考理科数学试卷2015届宁夏固原市第一中学高三最后冲刺模拟文科数学试卷2014-2015学年河南省确山县二中高二4月月考文科数学试卷2016届湖南省长沙市一中高三月考八理科数学试卷
12-13高三·河南南阳·阶段练习
9 . 如图,在
中,
是
的角平分线,
的外接圆交
于点
,
.
![](https://img.xkw.com/dksih/QBM/2016/6/7/1572696996036608/1572697002213376/STEM/a1d2f57cf6d74c838b101b1424485b37.png)
(1)证明:
;
(2)当
,
时,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0427054c47e348f35771872fd0215a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c71855e55064d1dc59eabe43e73a881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846071242f981289741ad19f4e7190cf.png)
![](https://img.xkw.com/dksih/QBM/2016/6/7/1572696996036608/1572697002213376/STEM/a1d2f57cf6d74c838b101b1424485b37.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679372e54c59c5cf67931b12b9833e02.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f7d9f5e71bfef8188b1216c1276c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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