1 . 选修4-1:几何证明选讲
如图,圆
是
的外接圆,
是
的中点,
交
于
.
![](https://img.xkw.com/dksih/QBM/2016/10/31/1573101706616832/1573101712711680/STEM/da5dea06400c4783b9c5f7d2caf7482a.png)
(Ⅰ)求证:
;
(Ⅱ)若
,点
到
的距离等于点
到
的距离的一半,求圆
的半径
.
如图,圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2333da32638ec636fa1e69e750ca4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e262f59351803e420bf1226c95e4bba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2016/10/31/1573101706616832/1573101712711680/STEM/da5dea06400c4783b9c5f7d2caf7482a.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c785dd3acc900f2df19930dcb0b816c.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73c03338db66b081700f70bcf9a0989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
2016-12-04更新
|
146次组卷
|
2卷引用:2017届湖南永州市高三高考一模考试数学(理)试卷
2 . 选修4-1:几何证明选讲
如图,四边形
外接于圆,
是圆周角
的角平分线,过点
的切线与
延长线交于点
,
交
于点
.
![](https://img.xkw.com/dksih/QBM/2016/9/12/1573015911538688/1573015918010368/STEM/e40e8d2e5f3446c2aeb156a47188a259.png)
(1)求证:
;
(2)若
是圆的直径,
,求
的长.
如图,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd777f9452cb8b56d8a0d3b07d15c19f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2016/9/12/1573015911538688/1573015918010368/STEM/e40e8d2e5f3446c2aeb156a47188a259.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73c8a92b36b72cc4441fd0a9013f841.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f03dab955d3953261e1f3f437f6128f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
3 . 选修4-1:几何证明选讲
如图,
为
的直径,过点
作
的切线
交
于点
的延长线交
于点
.
![](https://img.xkw.com/dksih/QBM/2016/12/22/1619402851647488/1619402852311040/STEM/4b8c1e8cfa464e90995e6a12224c36a1.png)
(1)求证:
;
(2)若
,求
和
的长.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eab767f07893891de2f6558d45e9b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07f3700c45a84b02f153ea0fb20b4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2016/12/22/1619402851647488/1619402852311040/STEM/4b8c1e8cfa464e90995e6a12224c36a1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283c87427f4af230ba9e20ba9446a922.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd2c6dbd4815508d9480ed15277fe5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
4 . 选修4-1:几何证明选讲
如图,
是
的直径,
是
上的点,
是
的平分线,过点
作
,交
的延长线于点
.
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573024802406400/1573024808894464/STEM/84902b9bf855499b96ba3e3e126b5b6a.png)
(1)求证:
;
(2)过
点作
,垂足为
,求证:
.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6062582a0a1679aa777451f25008411d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535a65c61f47d2b893706d4bc3499e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573024802406400/1573024808894464/STEM/84902b9bf855499b96ba3e3e126b5b6a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412e83a76b740809cc67f48053586e4c.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4fedfec2258cee649e03043bd45627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2d7f49c2ef973e8241da30b70104d6.png)
您最近一年使用:0次
2016-12-04更新
|
127次组卷
|
2卷引用:2016届湖南宁远县一中高三下学期模拟考试数学(理)试卷
5 . 选修4-1:几何证明选讲
如图,
是
的直径,
是
上一点,
切
于
交
于
,且
.
![](https://img.xkw.com/dksih/QBM/2016/9/12/1573015235788800/1573015242203136/STEM/e2556a61d5794858a6dc4e92a11ad788.png)
(1)求证:
与
相切;
(2)已知
与
交于
,
,求
的长.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b294bc03d584963d08ae46b7a10fad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61b1b4c9a546a94822a9a2684c20148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736da9ab559a1acd3fb37eebc5775f39.png)
![](https://img.xkw.com/dksih/QBM/2016/9/12/1573015235788800/1573015242203136/STEM/e2556a61d5794858a6dc4e92a11ad788.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc32ef00c21c5e77de637ced3ee1250a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
6 . 已知
是
的外角
的平分线, 交
的延长线于点
,延长
交
的外接圆于点
,连接
.
![](https://img.xkw.com/dksih/QBM/2016/11/18/1579006263427072/1579006264107008/STEM/f86357e968244460ba03d6bd37dc1d11.png)
(1)求证:
;
(2)若
是
外接圆的直径,
, 求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68806d81b6291afa517f3b6a58aa46b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa175408eddbdfddfbe9701646d62b92.png)
![](https://img.xkw.com/dksih/QBM/2016/11/18/1579006263427072/1579006264107008/STEM/f86357e968244460ba03d6bd37dc1d11.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07b92b8282c7fd1158b3b5098e38c39.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81eb721cdb5b39bd3b27e182c3647344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2016-12-04更新
|
170次组卷
|
5卷引用:2016届湖南省高考冲刺卷(理)(三)数学卷
7 . 如图,
是以
为直径的半圆上两点,且
.
![](https://img.xkw.com/dksih/QBM/2016/12/9/1579058766381056/1579058767118336/STEM/b5980541bc9741ae8a1e044087eb3434.png)
(1)若
,证明:直线
平分
;
(2)作
交
于
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dc18a16a5e136f2f2022d3cbed6776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522464a0aad5fbed92d01ccb9b01fb24.png)
![](https://img.xkw.com/dksih/QBM/2016/12/9/1579058766381056/1579058767118336/STEM/b5980541bc9741ae8a1e044087eb3434.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98c8e36238ad90378e724466fcb6023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90be2908153fa6e4d84afe7d4c955e5.png)
(2)作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736590304a98a696eab763d948ed05c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4508d8d0179798bb67b89433a3e310cd.png)
您最近一年使用:0次
2016-12-04更新
|
120次组卷
|
3卷引用:2016届湖南长沙市高三下一模考试数学(理)试卷
8 . 如图,已知
为圆
的一条直径,以端点
为圆心的圆交直线
于
两点,交圆
于
两点,过点
作垂直于
的直线,交直线
于
点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/4/88cf66ba-35c9-4877-8261-eda0916f10a8.png?resizew=189)
(1)求证:
四点共圆;
(2)若
,求
外接圆的半径.
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a21acc387aa273b83b8387baa73e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/4/88cf66ba-35c9-4877-8261-eda0916f10a8.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad8f0046014e9c9fcd1b341be7fc7f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f05d52a447e5ee79d99f1a7120a8adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e64c953aaf341e772a5fe776fbc78a.png)
您最近一年使用:0次
2016-12-03更新
|
382次组卷
|
5卷引用:2016届湖南师大附中高三下学期高考模拟三文科数学试卷