1 . 【选修4-1:几何证明选讲】
如图,P为圆外一点,PD为圆的切线,切点为D,AB为圆的一条直径,过点P作AB的垂线交圆于C、E两点(C、D两点在AB的同侧),垂足为F,连接AD交PE于点G.
![](https://img.xkw.com/dksih/QBM/2015/12/22/1572379169292288/1572379175657472/STEM/cf86b095aa2b4379b571f4206b676f07.png)
(1)证明:PG=PD;
(2)若AC=BD,求证:线段AB与DE互相平分.
如图,P为圆外一点,PD为圆的切线,切点为D,AB为圆的一条直径,过点P作AB的垂线交圆于C、E两点(C、D两点在AB的同侧),垂足为F,连接AD交PE于点G.
![](https://img.xkw.com/dksih/QBM/2015/12/22/1572379169292288/1572379175657472/STEM/cf86b095aa2b4379b571f4206b676f07.png)
(1)证明:PG=PD;
(2)若AC=BD,求证:线段AB与DE互相平分.
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2 . 如图,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
,连结
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/b88c8aa3-1254-4cbd-ad9c-f265eab76449.png?resizew=207)
(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/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6344778ed1e75c1a99e2268468081867.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/0faed94a64b2dcfc6801b4fca0f16675.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/editorImg/2023/1/6/b88c8aa3-1254-4cbd-ad9c-f265eab76449.png?resizew=207)
(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/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba4d0b54a0b2104e1c3a2061e4bffc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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3 . 如图,⊙O的半径OB垂直于直径AC,D为AO上一点,BD的延长线交⊙O于点E,过E点的圆的切线交CA的延长线于点P.
求证:PD2=PA•PC
求证:PD2=PA•PC
![](https://img.xkw.com/dksih/QBM/2018/11/16/2076809708109824/2078307597312000/STEM/23a2012e-b378-468a-81a7-84d80fbd22c3.png?resizew=186)
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4 . 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)
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5 . [选修41:几何证明选讲]
如图,
是圆
的切线,切点为
,
是过圆心
的割线且交圆
于
点,过
作圆
的切线交
于点
.
求证:
.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7720ba35de8581eb799fcaa81cfbaf8d.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5178fcc1a040999563466fd69ed8b69a.png)
![](https://img.xkw.com/dksih/QBM/2017/11/16/1818403876003840/1818423632052224/STEM/b970ed2b97bd4b7a84154cf5ec46c9f0.png?resizew=192)
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6 . 如图,
是圆
的切线,切点为
,
是过圆心
的割线且交圆
于点
,过
作圆
的切线交
于点
,
. 求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/e02a68a2e27f6c7a6d03f2fd7a602b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5178fcc1a040999563466fd69ed8b69a.png)
![](https://img.xkw.com/dksih/QBM/2017/12/16/1839787439570944/1841115563515904/STEM/44fde1f05ec4476e974e47f5a282586d.png?resizew=149)
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11-12高三上·江苏常州·期中
7 . 如图,从圆
外一点
作圆
的两条切线,切点分别为
,
与
交于点
,设
为过点
且不过圆心
的一条弦,求证:
四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff92ef23dd31bb91ece0b416b231fd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799701e69ccb3dc700fab43a5c10c78a.png)
![](https://img.xkw.com/dksih/QBM/2011/12/7/1570559776473088/1570559782223872/STEM/3e5a442a8f0e4b48b148b08354975012.png?resizew=183)
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8 . 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)
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9 . A.(几何证明选讲)
如图,
为圆
的直径,
在圆
上,
于
,点
为线段
上任意一点,延长
交圆
于
,
.
(1)求证:
;
(2)若
,求
的值.
如图,
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e68633cbbe3cc2d0801305f81a7aa86.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/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc9c9a1c828f5b3c718e2a98a749192.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b63745558b8ca67cd9a10cc85b00696.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea37f262f50b2c43b5c5fba506f3f39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9935fd41734aa307e947e119880e21.png)
![](https://img.xkw.com/dksih/QBM/2017/11/26/1825705412747264/1826888858271744/STEM/b3afa65ab2774f53a783b1296f48b881.png?resizew=143)
您最近一年使用:0次
2016-12-04更新
|
189次组卷
|
3卷引用:2016届广东省深圳市高三第二次调研考试数学(理)试卷