1 . 选修 4-1:几何证明选讲
已知点
在圆
直径
的延长线上,
切圆
于
点,
分别交
,
于点
,
,
.
![](https://img.xkw.com/dksih/QBM/2017/11/28/1827047244275712/1828939645018112/STEM/53a59f6801fe4ac4bb86594e47f541b4.png?resizew=171)
(1)求证:
为
的平分线;
(2)若
,求
的值.
已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd546aa376d38da2cfbae4a38dcbd01.png)
![](https://img.xkw.com/dksih/QBM/2017/11/28/1827047244275712/1828939645018112/STEM/53a59f6801fe4ac4bb86594e47f541b4.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78dc4f4584665f0db3d9363784c1683.png)
您最近一年使用:0次
2 . 如图,已知圆
是
的外接圆,
是
边上的高,
是圆
的直径.
![](https://img.xkw.com/dksih/QBM/2017/11/21/1822048528678912/1823292782215168/STEM/1f4e76b5f4194a3f8016675a3896e26a.png?resizew=167)
(1)求证:
;
(2)过点
作圆
的切线交
的延长线于点
,若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47d64e7cd6c3179394120d007ff12a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2017/11/21/1822048528678912/1823292782215168/STEM/1f4e76b5f4194a3f8016675a3896e26a.png?resizew=167)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed8f57d66aae0f646879f7b41bf0343.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0da7b2fff904812954936c341960a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
3 . 选修4-1:几何证明选讲
如图,
是⊙
直径,
与⊙
相切于
,
为线段
上一点,连接
分别交⊙
于![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/014153533fd64fdcad0f710ace30e110.png)
两点,连接
交
于点
.
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/627bb6e7d08c48dca54a88765db90602.png)
(1)求证:
四点共圆;
(2)若
为
的三等分点且靠近
,
,
,求线段
的长.
如图,
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/f4acbb2c672d49e5ac9d30aa8575117e.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/dc20e596c41f4de7ae393941513793b4.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/6860316ee54c4619a73cf84b3479cb34.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/dc20e596c41f4de7ae393941513793b4.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/5bfeb834a8de4d5fab2a35cb149d6082.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/ccb85bec02164fe3872be12f7f54b739.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/6860316ee54c4619a73cf84b3479cb34.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/83740875d0da43e3bf5be3872c343680.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/dc20e596c41f4de7ae393941513793b4.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/014153533fd64fdcad0f710ace30e110.png)
两点,连接
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/6770fcfb6bc94a9d93967171d7192129.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/6860316ee54c4619a73cf84b3479cb34.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/e94fdede599c45f9b5a2d415e0d1d2e3.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/627bb6e7d08c48dca54a88765db90602.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/45c887c2efca4d29a0aeec1bc9b04f0c.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/e94fdede599c45f9b5a2d415e0d1d2e3.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/62ee75e6328a40f79a945c90586f78f3.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/ccb85bec02164fe3872be12f7f54b739.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/c9b83bfb828a4160aecb9b4a60ffe6f6.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/9c1547e061dc4d89ac930b70bf3df7af.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101374464/STEM/54e91d13fa3043a7ab886a26107592af.png)
您最近一年使用:0次
4 . 选修4-1:几何证明选讲
如下图,四边形
内接于
,过点
作
的切线
交
的延长线于
,已知
.
![](https://img.xkw.com/dksih/QBM/2016/12/1/1573190598074368/1573190603907072/STEM/413d671276e44bc9a7ba456eae9ad2ce.png)
(Ⅰ)若
是
的直径,求
的大小;
(Ⅱ)若
,求证:
.
如下图,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2ce04e29ecab05af9c8d1b4c81d516.png)
![](https://img.xkw.com/dksih/QBM/2016/12/1/1573190598074368/1573190603907072/STEM/413d671276e44bc9a7ba456eae9ad2ce.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be04496b4e06b1c47d433d880b442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001fb1746a5c0d71c5d645e024fa8b3e.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ca81d66713ac3f0dcc6b1b3209b76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbe3f5c93f7c60104ca98978d5a3f45.png)
您最近一年使用:0次