1 . 选修4-1:几何证明选讲
如图,四边形
内接于圆,
,过
点的圆的切线与
的延长线交于
点.
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572494797832192/1572494803894272/STEM/070ab6f9faf6462792f9206cd1be4c80.png)
(1)求证:
;
(2)若
,求
的长.
如图,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532aece6cfd67e2a97977eed978dbf2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/2016/2/24/1572494797832192/1572494803894272/STEM/070ab6f9faf6462792f9206cd1be4c80.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572494797832192/1572494803894272/STEM/b1a6e9b6aa8647ad92224f8472607773.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572494797832192/1572494803894272/STEM/38eae9165f90432291f60f10faa2b4a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2016-12-04更新
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2 . 【选修4-1:几何证明选讲】
如图,已知圆上的弧
,过点
的圆的切线
与
的延长线交于
点.
![](https://img.xkw.com/dksih/QBM/2015/12/22/1572379801321472/1572379807793152/STEM/29a338a4b03445b8af5ca50d6467db10.png)
求证:(1)
;
(2)
.
如图,已知圆上的弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d153474afe208d90cc904f77f4579379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5402fd66f25b025c2f89c0897354d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc0983721388501807b32c17ca08281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ebbd866e455cf80ea669c9f56f792c.png)
![](https://img.xkw.com/dksih/QBM/2015/12/22/1572379801321472/1572379807793152/STEM/29a338a4b03445b8af5ca50d6467db10.png)
求证:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cccd81670438fe95436683b38680eda.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0f10c558c9651092742fc29c953f38.png)
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2012·辽宁大连·二模
3 . 已知
为半圆
的直径,
,
为半圆上一点,过点圆的切线
,过
点作
于
,交半圆于点
.
![](https://img.xkw.com/dksih/QBM/2016/1/15/1572438604488704/1572438610206720/STEM/f7850f4104584980a61f7e182b8cd92b.png)
(1)证明:
平分
;
(2)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/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96dae94a9c26b6dd1dbcdebd20373033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7b783dc89ca6934572319d2e9dfd22.png)
![](https://img.xkw.com/dksih/QBM/2016/1/15/1572438604488704/1572438610206720/STEM/f7850f4104584980a61f7e182b8cd92b.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd777f9452cb8b56d8a0d3b07d15c19f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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2010·黑龙江哈尔滨·一模
4 . 选修4-1:几何证明选讲
如图,已知
点在⊙
直径的延长线上,
切⊙
于
点,
是
的平分线,且交
于
点,交
于
点.
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f064c53e1030482cada14b5002913cf0.png)
(1)求
的度数;
(2)若
,求
.
如图,已知
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c9b96029815b4fee956f1dd14b16c519.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c195da6c33724175ad833081f8b6c367.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/658f5ce6c1c24beb9ee7d0862af41c9a.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c195da6c33724175ad833081f8b6c367.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/86e450de1d844ab085556f65f163d0bb.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/3b024db94d38400ab4778285d6a147ed.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/6636f6ff0f0e4d44b6f35a63393fc31d.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/babf31d6a39c44ffb64ca8294ab0d531.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/3f2d4c92974d4a60b3adeefacffd3664.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/4b016ec3d5b544bdbe4990ea634529a5.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/2140925fcb9a4e16937624eb1dfe90f1.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f064c53e1030482cada14b5002913cf0.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/0c51a0a5c8ab4cec8af8be1657b0c9b4.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/58bb7d54d6444190b394bbcc7be1aaeb.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f394ef40aaa64bbf9bba63b22333024d.png)
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