真题
1 . 选修4—1:几何证明选讲 如图,直线AB为圆的切线,切点为B,点C在圆上,∠ABC的角平分线BE交圆于点E,DB垂直BE交圆于D.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/5365865e-1cc9-47a2-9e47-f3464ca9a3c5.png?resizew=160)
(Ⅰ)证明:DB=DC;
(Ⅱ)设圆的半径为1,BC=
,延长CE交AB于点F,求△BCF外接圆的半径.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/5365865e-1cc9-47a2-9e47-f3464ca9a3c5.png?resizew=160)
(Ⅰ)证明:DB=DC;
(Ⅱ)设圆的半径为1,BC=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
2019-01-30更新
|
3916次组卷
|
12卷引用:2015届江西省吉安市第一中学高三上学期第二次阶段考试文科数学试卷
2015届江西省吉安市第一中学高三上学期第二次阶段考试文科数学试卷2013年全国普通高等学校招生统一考试理科数学(新课标1卷)2013年全国普通高等学校招生统一考试文科数学(新课标1卷)(已下线)2014年高考数学文二轮专题复习与测试选修4-1几何证明选讲练习卷(已下线)2014届甘肃省兰州一中高考模拟一理科数学试卷(已下线)2014届甘肃省兰州一中高考模拟一文科数学试卷2015届黑龙江省哈尔滨六中高三上学期期末考试理科数学试卷2015届陕西省西安长安区一中高三上学期第三次质检理科数学卷2015届陕西省西安长安区一中高三上学期第三次质检文科数学卷2016届甘肃省会宁县一中高三上第四次月考理科数学试卷2016届湖北省宜昌市一中高三上学期12月月考数学试卷河北省武邑中学2017届高三下学期第一次质检考试数学(文)试题
名校
2 . 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:江西省南昌市四校联盟2019-2020学年高三第二次联考数学(文)试题
3 . 选修4-1:几何证明选讲
如图,过圆
外一点
作一条直线与圆
交
两点,且
,作直线
与圆
相切于点
,连接
交
与点
,已知圆
的半径为2,
.
![](https://img.xkw.com/dksih/QBM/2016/10/31/1573102947753984/1573102953791488/STEM/265bd159d0374fecac19a6bd9be20eaa.png)
(1)求
的长;
(2)求证:
.
如图,过圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e6f98369bdaa02ee8e8685f8f23d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e390480dce825d6302a5223cd073d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a3b32f1db027d67ed28e5b2113e79d.png)
![](https://img.xkw.com/dksih/QBM/2016/10/31/1573102947753984/1573102953791488/STEM/265bd159d0374fecac19a6bd9be20eaa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d315eff37c1bdf5be90b6015b08bdea.png)
您最近一年使用:0次
4 . 选修4-1:几何证明选讲
如图所示,已知
为
的
边上一点,
经过点
,交
于另一点
,
经过点
,交
于另一点
与
交于点
.
![](https://img.xkw.com/dksih/QBM/2016/10/31/1573102650408960/1573102656995328/STEM/5a8f26291fdd46fbab413416b92528b9.png)
(1)求证:
;
(2)若
的半径为5,圆心
到直线
的距离为3,
切
于点
,求线段
的长.
如图所示,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6a2c03b88b9ac5d5641e30f64a462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8ef224337c60baeb1327f4f1973a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8065440f9e61ca5331e85cd9a5d8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8ef224337c60baeb1327f4f1973a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/2016/10/31/1573102650408960/1573102656995328/STEM/5a8f26291fdd46fbab413416b92528b9.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a4965e97e3994ac9702a73e1b2b3df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8ef224337c60baeb1327f4f1973a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da1da462918dd5eb035ae3efab21a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8ef224337c60baeb1327f4f1973a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
您最近一年使用:0次
5 . 选修4-1:几何证明选讲
如图,
是圆
的直径,
是圆内接四边形,
于点
,且
与圆
相切于点
.
![](https://img.xkw.com/dksih/QBM/2016/9/13/1573018779394048/1573018785505280/STEM/101a2ed377a0413888a894678a05d66f.png)
(1)求证:
平分
;
(2)若
,求
的长.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259c150cffdc68e8ba79848110cf7d57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2016/9/13/1573018779394048/1573018785505280/STEM/101a2ed377a0413888a894678a05d66f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89a98486b422ac7c9e4d977d6817b26.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b971966a4483b0c2a56279e34a78fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2016-12-04更新
|
92次组卷
|
2卷引用:2017届江西新余一中高三上学期开学考试数学(理)试卷
6 . 选修4-1:几何证明选讲
如图,已知
与圆
相切,
为切点,
为割线,弦
,
相交于
点,
为
上一点,且
.
![](https://img.xkw.com/dksih/QBM/2016/9/12/1573014847234048/1573014853287936/STEM/7a652be337cc4d25a7aab4a6d67b6a64.png)
(1)求证:
四点共圆;
(2)若
,
,求
的长.
如图,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.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/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41bcbf7a137218daf88f1deddd2adc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994e2fc5676a42e4edba54a291236d7c.png)
![](https://img.xkw.com/dksih/QBM/2016/9/12/1573014847234048/1573014853287936/STEM/7a652be337cc4d25a7aab4a6d67b6a64.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21a511ffe1a6617f45c48748a16372cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5a0689f27f06ebd8468e4a5cbab799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034a9d2e093d0040c609450c3a344cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
您最近一年使用:0次
7 . 选修4-1:几何证明选讲
如图,
的外接圆为⊙
,延长
至
,再延长
至
,使得
成为
,
的等比中项.
![](https://img.xkw.com/dksih/QBM/2016/9/8/1573005992738816/1573005998833664/STEM/afe72850fd8b4cefba8a1d18eb32eaa0.png)
(1)求证:
为⊙
的切线;
(2)若
恰好为
的平分线,
,
,求
的长度.
如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350e954f629c1901a5cec03558319e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://img.xkw.com/dksih/QBM/2016/9/8/1573005992738816/1573005998833664/STEM/afe72850fd8b4cefba8a1d18eb32eaa0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1b4d52dc296acb2764f333bd4343f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
您最近一年使用:0次
8 . 选修4—1几何证明选讲
如图,已知直线
与圆
切于点
,直线
过圆心
,且与圆
交于点
,若
.
![](https://img.xkw.com/dksih/QBM/2016/8/3/1572946486329344/1572946492702720/STEM/d89f0928436c4399bf3741489684cdd9.png)
(1)求
的大小;
(2)若
的平分线与
交于点
,与圆
的另一个交点为
,求
.
如图,已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.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/d2be49c37e30a3ced0364c3e74d8c687.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/535a43e386263720545413ced24dd9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae9840f36e04cac85f07c3627afc9c2.png)
![](https://img.xkw.com/dksih/QBM/2016/8/3/1572946486329344/1572946492702720/STEM/d89f0928436c4399bf3741489684cdd9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2025e548509be905d2777f4479f195.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6062582a0a1679aa777451f25008411d.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47050d71aa1c86a620646c6860a96e90.png)
您最近一年使用:0次
名校
9 . 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
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507次组卷
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3卷引用:2016届江西省上高二中高三第七次月考文科数学试卷
10 . 如图所示,
为
的直径,
为
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572606939684864/1572606946131968/STEM/0f36bdb6092143fdbd45e998e383d0df.png)
(1)求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572606939684864/1572606946131968/STEM/a574bb09e86c4f8595213823afe10cd7.png)
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572606939684864/1572606946131968/STEM/f857367adba94f559aa6c6a3f7d5b434.png)
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572606939684864/1572606946131968/STEM/0f36bdb6092143fdbd45e998e383d0df.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572606939684864/1572606946131968/STEM/7b97f5a3ed28437fa31c23ff15ad4d14.png)
(2)求证:
![](https://img.xkw.com/dksih/QBM/2016/4/28/1572606939684864/1572606946131968/STEM/3b32ae06b8ad4a0dbe3dd7e6bee001ab.png)
您最近一年使用:0次