1 . 选修4-1:几何证明选讲
如图所示,PA为圆O的切线,A为切点,PO交圆O于B,C两点,PA=20,PB=10,
的角平分线与BC和圆O分别交于点D和E.
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921527808/STEM/a6f051823ba8498787b5910e8caec0d4.png)
(1)求证:
;
(2)求
的值.
如图所示,PA为圆O的切线,A为切点,PO交圆O于B,C两点,PA=20,PB=10,
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921527808/STEM/85a4f1bd192a4dda92a850d70557e29a.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921527808/STEM/a6f051823ba8498787b5910e8caec0d4.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921527808/STEM/03f8537188fc4981a4f5aa32a2699264.png)
(2)求
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572969915473920/1572969921527808/STEM/90d6eafc4faf4ae0b5595927cb41d87f.png)
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10-11高二下·河南郑州·阶段练习
2 . .选修4-1:几何证明选讲
已知
ABC中,AB=AC, D是
ABC外接圆劣弧AC弧上的点(不与点A,C重合),延长BD至E.
(1)求证:AD的延长线平分
CDE;
(2)若
BAC=30°,
ABC中BC边上的高为2+
,
求
ABC外接圆的面积.
已知
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/b18484264a8a4d4b96a55e77f757e548.png)
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/b18484264a8a4d4b96a55e77f757e548.png)
(1)求证:AD的延长线平分
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/fb0457dd18ff453aa76a046a9e445e0a.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/fb0457dd18ff453aa76a046a9e445e0a.png)
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/b18484264a8a4d4b96a55e77f757e548.png)
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/4e5551f105934d3a9c4ebe6be17ac12d.png)
求
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/b18484264a8a4d4b96a55e77f757e548.png)
![](https://img.xkw.com/dksih/QBM/2012/3/22/1570818204868608/1570818210324480/STEM/37f0b721192d4235a13bfbfd0f01f5d5.png)
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2011·河南洛阳·一模
3 . 在△ABC中,AB=AC,过点A的直线与其外接圆交于点P,交BC延长线于点D.
(1)求证:
;
(2)若AC=3,求AP•AD的值.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f44caa95b907ab06f85da6f52b9213.png)
(2)若AC=3,求AP•AD的值.
![](https://img.xkw.com/dksih/QBM/2011/2/28/1570019776937984/1570019782385664/STEM/9c20ec07a9c642d29d236e8536c83727.png?resizew=252)
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2011·河南郑州·二模
4 . 选修4—1:几何证明选讲
如图,在△ABC中,∠C为钝角,点E,H分别是边AB上的点,点K和M分别是边AC和BC上的点,且AH=AC,EB=BC,AE=AK,BH=BM.
(Ⅰ)求证:E、H、M、K四点共圆;
(Ⅱ)若KE=EH,CE=3,求线段KM的长.
如图,在△ABC中,∠C为钝角,点E,H分别是边AB上的点,点K和M分别是边AC和BC上的点,且AH=AC,EB=BC,AE=AK,BH=BM.
(Ⅰ)求证:E、H、M、K四点共圆;
(Ⅱ)若KE=EH,CE=3,求线段KM的长.
![](https://img.xkw.com/dksih/QBM/2011/3/28/1570082402541568/1570082408013824/STEM/64dafb1f36b44094932560ebad332554.png?resizew=225)
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5 . 已知四边形
为圆
的内接四边形,且
,其对角线
与
相交于点
.过点
作圆
的切线交
的延长线于点
.
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/eba0a85b01e443c2872a5fca74406206.png)
(I)求证:
;
(II)若
,求证:
.
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/c1aed038f3534498a437fe4656651362.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/6884ebf765214e92a3e51ec95c828f57.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/04aba819001943faa0f602bf04b52fcb.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/c64b71f098554966b9f0db23c34d8d4e.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/686b6e79fc4f48168df06a59eec23ad7.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/0969e595ed0f4cf5b40bb168819e5c0f.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/e9872bc905294bfa87593165c3dba318.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/6884ebf765214e92a3e51ec95c828f57.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/f1f9a96b87df4ef8840213699c1cb76d.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/575ee7c8e9b1459088170c982ef5995d.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/eba0a85b01e443c2872a5fca74406206.png)
(I)求证:
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/8b7ee8d20a934c459254b2c1545bc938.png)
(II)若
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/68e8fe3a01f3491cb934548f68708c70.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572683042848768/1572683049271296/STEM/0e0ebf40db8942f69c7673c7643690f3.png)
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2013·河南郑州·一模
6 . 如图,在△ABC中,CD是∠ACB的平分线,△ACD的外接圆交BC于点E,AB=2AC.
![](https://img.xkw.com/dksih/QBM/2016/3/28/1572560111501312/1572560117145600/STEM/e1066d69f14c4558aded214b8d4dc80a.png)
(Ⅰ)求证:BE=2AD;
(Ⅱ)当AC=1,EC=2时,求AD的长.
![](https://img.xkw.com/dksih/QBM/2016/3/28/1572560111501312/1572560117145600/STEM/e1066d69f14c4558aded214b8d4dc80a.png)
(Ⅰ)求证:BE=2AD;
(Ⅱ)当AC=1,EC=2时,求AD的长.
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2016-12-02更新
|
376次组卷
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5卷引用:2014届河南省中原名校联盟高三上学期第一次摸底考试理科数学试卷
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2011·河南·一模
7 . 如图,已知AD是△ABC的外角∠EAC的平分线,交BC的延长线于点D,延长DA交△ABC的外接圆于点F,连接FB,FC.
(1)求证:FB=FC;
(2)求证:FB2=FA•FD;
(3)若AB是△ABC外接圆的直径,且∠EAC=120°,BC=6,求AD的长.
(1)求证:FB=FC;
(2)求证:FB2=FA•FD;
(3)若AB是△ABC外接圆的直径,且∠EAC=120°,BC=6,求AD的长.
![](https://img.xkw.com/dksih/QBM/2011/4/16/1570120503336960/1570120508833792/STEM/006578c216cd435bbee6e3d487477cea.png?resizew=213)
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2012·河南焦作·一模
8 . 在
中,AB=AC,过点A的直线与其外接圆交于点P,交BC延长线于点D.
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/13cf603650fe4de19d4d0d65cea4b9fc.png)
(1)求证:
;
(2)若AC=3,求
的值.
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/4068bd6d669d4586b69702cb3762e8c2.png)
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/13cf603650fe4de19d4d0d65cea4b9fc.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/0a245338e40a4c728e67305b45866c4f.png)
(2)若AC=3,求
![](https://img.xkw.com/dksih/QBM/2012/7/12/1570923707105280/1570923712651264/STEM/3d841a1467fa49a59809ed6a011bc517.png)
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2016-12-02更新
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