1 . 如图,直线
与直径为4的圆
交于
两点,且
,直线
切圆
于点
.
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040539918336/1573040546463744/STEM/47971440866b4a2d9aa8673b8c23c188.png)
(1)证明:
;
(2)若
,延长
交
于点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2899e607479d8d1c47d954ae9ebb7144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/2016/9/26/1573040539918336/1573040546463744/STEM/47971440866b4a2d9aa8673b8c23c188.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a109c829d652632a88ade6924fcda206.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d36d529ae753d360c14b243c1ef7992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18addf44c31c2dc0e4905b365e4801a0.png)
您最近一年使用:0次
2 . 选修4-1:几何证明选讲
如图,直线
与直径为4的圆
交于
两点,且
,直线
切圆
于点
.
![](https://img.xkw.com/dksih/QBM/2016/7/27/1572944464273408/1572944470859776/STEM/dbd9a8da005542edb6fba48949c0d25a.png)
(1)证明:
;
(2)若
,延长
交
于点
,求证:
.
如图,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2899e607479d8d1c47d954ae9ebb7144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/2016/7/27/1572944464273408/1572944470859776/STEM/dbd9a8da005542edb6fba48949c0d25a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a109c829d652632a88ade6924fcda206.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d36d529ae753d360c14b243c1ef7992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18addf44c31c2dc0e4905b365e4801a0.png)
您最近一年使用:0次
3 . 如图,
是圆
的直径,
是圆
上的两点,
,过点
作圆
的切线
交
的延长线于点
,连接
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/067ddae1-2207-4de1-98a3-1089ca3635ef.png?resizew=176)
(1)求证:
;
(2)若
,试求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9aa3f533894ca87a394f7a1dfd0ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771b610e4ddefa739a985d1e5462ce5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/067ddae1-2207-4de1-98a3-1089ca3635ef.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0832663dc2ac31bb883db666b58c2da.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f2f7183e51aa2ec919cc0e51df5ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
您最近一年使用:0次
2019-06-24更新
|
314次组卷
|
2卷引用:【校级联考】云南省曲靖市陆良县2019届高三上学期第一次摸底考试数学(文)试题
真题
4 . 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)
您最近一年使用:0次
2019-01-30更新
|
1681次组卷
|
6卷引用: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
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
5 . 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.
您最近一年使用:0次
2019-01-30更新
|
1079次组卷
|
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)
6 . 如图,圆
的半径
垂直于直径
,
为线段
上一点(不含端点),
的延长线交圆
于点
,过点
的切线交
的延长线于点
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/4/1e5f5a5f-0fb2-4fdf-b15e-7b44c6eba50a.png?resizew=171)
(1)求证:
;
(2)若
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859b5cf692e4d5d9d0f606248f2304fa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/4/1e5f5a5f-0fb2-4fdf-b15e-7b44c6eba50a.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb2781ac5895b0290b1fa42df0ded48.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae41d6dec0dd165af16aa9b12498cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c912595239412b2428fb1da0227717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c19fa4cd646f4d877c3e58cc346651.png)
您最近一年使用:0次
2011·河南商丘·二模
名校
7 . 选修4—1,几何证明选讲
如图所示,圆
的两弦
和
交于点
,
∥
,
交
的延长线于点
,
切圆
于点
.
(1)求证:△
∽△
;
(2)如果
,求
的长.
如图所示,圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.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/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/5639eeaf-f09e-4d54-803c-038e6a4210ed.png?resizew=126)
(1)求证:△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38a6341dbb03ec2c0c10e5353a07c7a.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a917db13b0c7bb4a4f81c81a970454c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2016-12-03更新
|
521次组卷
|
6卷引用:2015届云南省弥勒市高三年级模拟测试一理科数学试卷
2015届云南省弥勒市高三年级模拟测试一理科数学试卷2015届云南省弥勒市高三年级模拟测试一文科数学试卷(已下线)2011届河南省商丘市高三第二次模拟考试数学理卷(已下线)2014届高考数学总复习考点引领+技巧点拨选修4-1第2课时练习卷宁夏石嘴山市第三中学2016届高考一模数学(文)试题宁夏石嘴山市第三中学2016届高考一模数学(理)试题
2014·云南玉溪·一模
8 . 选修4-1:几何证明选讲
已知在
中,
是
上一点,
的外接圆交
于
,
.
(1)求证:
;
(2)若
平分
,且
,求
的长.
已知在
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/e4c0a24f60f54fba9e3b3a02ba479d2d.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/b4c74d332fc74422be37cdfbb9e3967a.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/cb9130aeaf624e25b4b12b08c778fc33.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/e91de764727049a3ba0c0f1ddb208e59.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/785ccb658d4f4b448aa30c73ba72fa94.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/63da89a00be740f0aa79b81988f2d523.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/4552ad8bb1ba4e36931a3659f81c134f.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/ae040982e00949dd8c9e3f5c51342a7c.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/e23da194ad98488aba2c4ab933ebbeb0.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/0ed73771867e411db6e535c47e0531ea.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/76edff6065c2407398d917cdff33c1b9.png)
![](https://img.xkw.com/dksih/QBM/2014/12/26/1571938673139712/1571938678816768/STEM/39d1d50da5794a7884b7a4a73043f400.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/8b287c44-9ed6-4479-8b3d-3ba97c3a40a8.png?resizew=169)
您最近一年使用:0次
2014·吉林·模拟预测
9 . 【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)
您最近一年使用:0次
2016-12-03更新
|
168次组卷
|
4卷引用: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