名校
1 . 在平面直角坐标系中,将曲线
上的每一个点的横坐标保持不变,纵坐标缩短为原来的
,得到曲线
,以坐标原点
为极点,
轴的正半轴为极轴,建立极坐标系,
的极坐标方程为
.
(1)求曲线
的参数方程;
(2)过原点
且关于
轴对称的两条直线
与
分别交曲线
于
和
,且点
在第一象限,当四边形
周长最大时,求直线
的普通方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f917a2022014d9c19c29eeac84c74e2f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e478787ebfeb68a5a7594dbd9eecd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f90eb172dbd2ff7ae6f705801c0737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
2017-04-15更新
|
1238次组卷
|
7卷引用:2017届河北省石家庄市高三一模考试(文科)数学试卷
2 . 选修4-1:几何证明选讲
如图,在圆内接梯形
中,
,过点
作圆的切线与
的延长线交于点
,若
.
![](https://img.xkw.com/dksih/QBM/2016/11/9/1573135186075648/1573135192621056/STEM/372423e4bab74565b97a7e6485573625.png)
(1)求证:梯形
为等腰梯形;
(2)求弦
的长.
如图,在圆内接梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e2dbfad0bc120f503e4d23b384280.png)
![](https://img.xkw.com/dksih/QBM/2016/11/9/1573135186075648/1573135192621056/STEM/372423e4bab74565b97a7e6485573625.png)
(1)求证:梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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3 . 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/2016/5/9/1572625066704896/1572625072816128/STEM/de6fa6317d364901817490bd3f2571aa.png)
(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/dd936a2405709574af0a73543d94ad9c.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/2016/5/9/1572625066704896/1572625072816128/STEM/de6fa6317d364901817490bd3f2571aa.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/f2fa1e4d40994e2e86c45eba0159a68f.png)
(2)过点
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/7c22a079c5f945cb925441033bbf1d30.png)
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/0d679278c1b14071a0c0973e3b5ca669.png)
![](https://img.xkw.com/dksih/QBM/2016/5/9/1572625066704896/1572625072816128/STEM/0eed3d0155cb4612b71d2d17bf6712e5.png)
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名校
4 . 如图,直线PQ与⊙O相切于点A,AB是⊙O的弦,∠PAB的平分线AC交⊙O于点C,连结CB,并延长与直线PQ相交于点Q,若AQ=6,AC=5.
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572607145648128/1572607151489024/STEM/0359539e1f0c4416859950790998664e.png)
(Ⅰ)求证:QC2﹣QA2=BC
QC;
(Ⅱ)求弦AB的长.
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572607145648128/1572607151489024/STEM/0359539e1f0c4416859950790998664e.png)
(Ⅰ)求证:QC2﹣QA2=BC
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b18d78c40ce368f60208949c5ae3fb.png)
(Ⅱ)求弦AB的长.
您最近一年使用:0次
2016-12-04更新
|
507次组卷
|
3卷引用:2016届河北省衡水中学高三下学期二调考试理科数学试卷
5 . 选修4-1:几何证明选讲:
如右图,圆
与圆
内切于点
,其半径分别为3与2,圆
的弦
交圆
于点
(
不在
上),
是圆
的一条直径.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/0ea025a9-b7c5-440b-8e7c-b79a6983bbd9.png?resizew=187)
(Ⅰ)求
的值;
(Ⅱ)若
,求
到弦
的距离.
如右图,圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/0ea025a9-b7c5-440b-8e7c-b79a6983bbd9.png?resizew=187)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746853ea6d76bd7cccc6bdd6c739aed7.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
6 . 选修4-1:几何证明选讲
如图,
是圆
的直径,
是圆
上两点,
与
相交于点
,
,
是圆
的切线,点
在
的延长线上,且
.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/3/ba1427b3-a8d2-411d-a18d-702ae388248c.png?resizew=147)
(1)
四点共圆;
(2)
.
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/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e5f736b1195fef1d2d300168a795f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8f887360a533f0a25b0b34fb11f0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbaa12e10837b302535b3331f08b2495.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/3/ba1427b3-a8d2-411d-a18d-702ae388248c.png?resizew=147)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54583088b8451cdc5ae13b739a8eebb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dfb0a85bb6aee4a1d8fc1abad4eecb.png)
您最近一年使用:0次
2016-12-03更新
|
338次组卷
|
3卷引用:2016届河北省邯郸市一中高三下学期研七考试文科数学试卷
2012·辽宁大连·二模
7 . 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)
您最近一年使用:0次
2016-12-03更新
|
694次组卷
|
13卷引用:2012届河北省唐山一中高三第一次高考仿真测试文科数学试卷
(已下线)2012届河北省唐山一中高三第一次高考仿真测试文科数学试卷(已下线)2012届辽宁省大连市沈阳市高三第二次模拟考试理科数学试卷(已下线)2014届云南省红河州高三毕业生复习统一检测理科数学试卷(已下线)2014届云南省红河州高三毕业生复习统一检测文科数学试卷2016届宁夏六盘山高级中学高三第一次模拟考试理科数学试卷(已下线)2015届河南省八校高三上学期第一次联考理科数学试卷2016届安徽省马鞍山二中等高三第三次联考理科数学试卷2016届安徽省马鞍山二中等高三第三次联考文科数学卷2016届贵州省贵阳市一中高三第四次月考理科数学试卷2016届贵州省贵阳市一中高三第四次月考文科数学试卷2016届海南省文昌中学高三上学期期末考试文科数学试卷2016届湖北省襄阳市高三上学期期末理科数学试卷福建省2016届高三毕业班总复习(几何选讲)单元过关形成性测试卷(文理科)数学试题
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)
您最近一年使用:0次
2016-12-02更新
|
349次组卷
|
9卷引用:2012届河北省唐山一中高三第一次高考仿真测试理科数学试卷
(已下线)2012届河北省唐山一中高三第一次高考仿真测试理科数学试卷(已下线)2012届河南省焦作市高三第一次质量检测理科数学试卷(已下线)2012届河南省焦作市高三第一次质量检测文科数学试卷(已下线)2012届黑龙江省哈六中高三第三次模拟考试理科数学试卷(已下线)2013届甘肃省河西五市部分普通高中高三第二次(5月)联考理科数学试卷2015届宁夏固原市第一中学高三最后冲刺模拟文科数学试卷(已下线)2014届云南部分名校(玉溪一中)高三11月月考理科数学试卷2014-2015学年河南省确山县二中高二4月月考文科数学试卷2016届湖南省长沙市一中高三月考八理科数学试卷
2013·河北唐山·三模
9 . 如图,AB是圆O的直径,C,D是圆O上两点,AC与BD相交于点E,GC,GD是圆O的切线,点F在DG的延长线上,且
.求证:
(Ⅰ)D、E、C、F四点共圆; (Ⅱ)![](https://img.xkw.com/dksih/QBM/2013/8/30/1571334802751488/1571334808125440/STEM/27a75bc4eaa1470cbd90c3a339eaba96.png)
![](https://img.xkw.com/dksih/QBM/2013/8/30/1571334802751488/1571334808125440/STEM/8b2d2c29bc3241be96d0c1461e73ab77.png)
(Ⅰ)D、E、C、F四点共圆; (Ⅱ)
![](https://img.xkw.com/dksih/QBM/2013/8/30/1571334802751488/1571334808125440/STEM/27a75bc4eaa1470cbd90c3a339eaba96.png)
![](https://img.xkw.com/dksih/QBM/2013/8/30/1571334802751488/1571334808125440/STEM/09374958012448759d3a6343378d06c4.png)
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2012·河北衡水·一模
10 . 如图,
是圆的两条平行弦,
,
交
于
、交圆于
,过
点的切线交
的延长线于
,
,
.
![](https://img.xkw.com/dksih/QBM/2013/1/21/1571105310400512/1571105316200448/STEM/07621d023a264552a14e51ad914afbed.png)
(1)求
的长;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d1ee2efdb2c3b7c90198efc88010db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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(1)求
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(2)求证:
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