1 . 如图,已知Rt△ABC,∠ABC=90°,D是AC的中点,⊙O经过A,B,D三点,CB的延长线交⊙O于点E,过点E作⊙O的切线,交AC的延长线于点F.在满足上述条件的情况下,当∠CAB的大小变化时,图形也随着改变,但在这个变化过程中,有些线段总保持着相等的关系.
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844531200/STEM/0591bcb2e32041fca413dbc5eaf15a7c.png?resizew=104)
(1)连接图中已标明字母的某两点,得到一条新线段与线段CE相等,并说明理由;
(2)若CF=CD,求sin F的值.
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844531200/STEM/0591bcb2e32041fca413dbc5eaf15a7c.png?resizew=104)
(1)连接图中已标明字母的某两点,得到一条新线段与线段CE相等,并说明理由;
(2)若CF=CD,求sin F的值.
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2 . 如图,已知AB切⊙O于B,BC是⊙O的直径,AC交⊙O于D,DE是⊙O的切线,CE⊥DE于E,DE=3,CE=4,求AB的长.
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844514816/STEM/be063f0aebf649ecad15635038670570.png?resizew=83)
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3 . 如图,AB是⊙O的直径,C为半圆上一点,CD⊥AB于D,若BC=3,AC=4,则AD∶CD∶BD等于( )
A.4∶6∶3 | B.6∶4∶3 |
C.4∶4∶3 | D.16∶12∶9 |
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4 . 如图,在⊙O中,半径OA⊥OB,弦AC交OB于D,E是OB延长线上一点,若∠OAD=30°,ED=CE.
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844482048/STEM/9a07340cbd6e4d71a9d2f0f483af0ad2.png?resizew=75)
求证:EC是⊙O的切线.
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844482048/STEM/9a07340cbd6e4d71a9d2f0f483af0ad2.png?resizew=75)
求证:EC是⊙O的切线.
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5 . 如图,已知P是⊙O外一点,PD为⊙O的切线,D为切点,割线PEF经过圆心O,若PF=12,PD=4
,则圆O的半径长为________ 、∠EFD的度数为________ .
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844449280/STEM/50babfa772ae4afb895ef814fd2be01d.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844449280/STEM/2e59fdd541db4f05b9668561ec290cfb.png?resizew=123)
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6 . 如图,四边形ABCD为圆内接四边形,AC为BD的垂直平分线,∠ACB=60°,AB=a,则CD等于( )
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844408320/STEM/7aedc0bac21d4ba08abc492881e89365.png?resizew=91)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844408320/STEM/7aedc0bac21d4ba08abc492881e89365.png?resizew=91)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 如图,已知⊙O是△ABC的外接圆,⊙I是△ABC的内切圆,∠A=80°,则∠BIC等于( )
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844359168/STEM/521861ea16274fc4a18fcb5d732a1b34.png?resizew=105)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848846274560/1815497844359168/STEM/521861ea16274fc4a18fcb5d732a1b34.png?resizew=105)
A.80° | B.100° | C.120° | D.130° |
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名校
8 . 如图,
、
分别是圆
的切线和割线,其中
为切点,
为切线
的中点,弦
、
相交于点
,弦
延长线上的点
,满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/0b3bbc2f154292f5d767fa24bc3f9d9d.png)
求证:、
、
三点共线的充分必要条件是
、
、
三点共线.
![](https://img.xkw.com/dksih/QBM/2017/8/2/1743616646004736/1745775321595904/STEM/de21a44633ca449299815c7b70691184.png?resizew=214)
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9 . 已知圆
的圆心在直线
上,且与直线
相切于点
.
(1)求圆
方程;
(2)是否存在过点
的直线
与圆
交于
两点,且
的面积是
(
为坐标原点),若存在,求出直线
的方程,若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/17bcff775c514a90ab3a7c00c05e5804.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/b80885e74ae74f6eb7b2e83a9e9fde44.png?resizew=56)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/2af23dd6926f42f3b314cad33be57d67.png?resizew=80)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/7de8e1ece3f7402999f8be17b1ecec33.png?resizew=55)
(1)求圆
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/266fd6493b74449a9393cd53af96cdca.png?resizew=16)
(2)是否存在过点
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/162da034c64b4798a3b2322f7cc5d5a4.png?resizew=47)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/bb698ee86a704367875ceac8fbc7d407.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/79aeee873f904ac78297c6cd758e9b1e.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/6fe06310008a4ade9d255196a0b1e736.png?resizew=33)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/a993fd466e894c92840bb4880918a57c.png?resizew=48)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/01872a498b8f4b649460be9830570e85.png?resizew=33)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/fb588859b4ec4d56a85b9e7ea8d3295a.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2017/10/6/1789486270971904/1790156898983936/STEM/9cdcfa3c836b47c2aa4bef8fc5bbf81e.png?resizew=9)
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10 . 选修4-1:几何证明选讲
选修
:几何证明选讲
如图,
为
上的三个点,
是
的平分线,交
于点
,过
作
的切线交
的延长线于点
.
(Ⅰ)证明:
平分
;
(Ⅱ)证明:
.
选修
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb420ded9d68ae6486ae8c617a3636d.png)
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7095a91b7486c5299db97f9eacb7494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7095a91b7486c5299db97f9eacb7494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7095a91b7486c5299db97f9eacb7494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79cd9d0d73549e2944578f3513631ce5.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3432942a9079e1554cb5d236050b102e.png)
![](https://img.xkw.com/dksih/QBM/2017/7/8/1732926196006912/1790246060294144/STEM/90e766aa544b4d36b9dc2506bbc30438.png?resizew=124)
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2017-10-08更新
|
114次组卷
|
2卷引用:福建省2016届高三基地校总复习综合卷数学试题(厦门双十、南安一中、厦门海沧实验中学文科)