1 . 已知直线
:
和圆
:
.
(1)判断直线
和圆
的位置关系,并求圆
上任意一点
到直线
的最大距离;
(2)过直线
上的点
作圆
的切线
,切点为
,求证:经过
,
,
三点的圆与圆
的公共弦必过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7fbfa2214ca72495a993b2fed8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6980c1b60505861f5dda0faaecbd78d8.png)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2024-01-12更新
|
207次组卷
|
2卷引用:甘肃省2023-2024学年高二上学期1月期末学业质量监测数学试题
2 . 已知x轴平分的一个内角,
,
,
的外接圆为圆M.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)证明圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/622b0046e69150d7ea8ab7b0aee1716c.png)
您最近一年使用:0次
名校
解题方法
3 . 已知圆
和圆
.
(1)求证:圆
和圆
相交;
(2)求圆
与圆
的公共弦所在直线的方程及公共弦的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f18415494d6e521ed30ed3f40ce28f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cb795a78ee91833445b70ae3293c70.png)
(1)求证:圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2024-01-23更新
|
300次组卷
|
3卷引用:云南省昭通市一中教研联盟2023-2024学年高二上学期期末质量检测数学试题(B卷)
名校
解题方法
4 . 已知圆C:
和直线l:
相切.
(1)求圆C半径
;
(2)若动点M在直线
上,过点M引圆C的两条切线MA、MB,切点分别为A、B.
①记四边形MACB的面积为S,求S的最小值;
②证明直线AB恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dceb22241e283787a43ac2b006ee56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b905d12adb1d83dd79b0b6512a32ab.png)
(1)求圆C半径
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)若动点M在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446ffa300bde93a7f64368cb43bd3551.png)
①记四边形MACB的面积为S,求S的最小值;
②证明直线AB恒过定点.
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2024-04-14更新
|
405次组卷
|
3卷引用:云南省昆明市官渡区2022-2023学年高二上学期期中联考数学试卷
解题方法
5 . 已知圆
过点
,圆心
在直线
上,且圆
与
轴相切.
(1)求圆
的方程;
(2)已知圆
与圆
交于
、
两点,过直线
上(除线段
部分)一点
分别作两圆的切线,切点分别为点
、
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8238bb883f17fcc90b77ba80c4d14916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09324568f2f3995b2f932e66ee5926ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4eab07c6bb565a07aa4278862f75a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/2189887d9bc110b8a409df20ec4d827a.png)
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6 . 已知圆
.
(1)证明:圆C过定点;
(2)当
时,点P为直线
上的动点,过P作圆C的两条切线,切点分别为A,B,求四边形
面积最小值,并写出此时直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3316cc2e087e26cd645cd8f8c8431704.png)
(1)证明:圆C过定点;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d33af76688e9ad91038976fc0e6d252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283b0cef5d644b8dceb910ce2c76f21c.png)
您最近一年使用:0次
解题方法
7 . 已知圆
,圆
,证明圆
与圆
相交,并求圆
与圆
的公共弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0d9aa06aae653c5d9206ceefd7df7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9444c86466e14ecbaf69c7647b7d4835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
名校
8 . 已知圆C:
,
.
(1)证明:圆C过定点.
(2)当
时,过
作圆C的两条切线,切点分别为A,B,求直线AB的方程;
(3)当
时,若直线l:
与圆C交于M,N两点,且
,其中O为坐标原点,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57352787959c24318b6b164e55bae277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd9736828195f010db4e1f0a9dea7a4.png)
(1)证明:圆C过定点.
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21b59d92c33a3b451d6cc13878c45.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231896d2386c924306fce5ccf9f9e8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331c27b493b12fc43837085e9bcfd83d.png)
您最近一年使用:0次
2023-11-09更新
|
607次组卷
|
3卷引用:河北省保定市定州市2023-2024学年高二上学期期中数学试题
9 . 已知圆
,直线
.
(1)若点P在直线l上运动,过点P作圆O的两条切线
,切点分别为
,求证:过点
的圆过定点,并求出所有定点的坐标;
(2)若点P在直线l上运动,过点P作圆O的两条切线
,切点分别为
,求证:直线AB过定点,并求出定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1bba341d6dc102851c557072f738ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82503069ae1dda33bb96fdddbe1c87c6.png)
(1)若点P在直线l上运动,过点P作圆O的两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e7f54c3c611633cf0e2fe218d89460.png)
(2)若点P在直线l上运动,过点P作圆O的两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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名校
10 . 已知圆
与圆
.
(1)求证:圆
与圆
相交;
(2)求两圆公共弦所在直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9ef0be8a07b1c9066e9870a8bddbd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c3af319e9974254c266b70cad677076.png)
(1)求证:圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)求两圆公共弦所在直线的方程.
您最近一年使用:0次
2023-09-02更新
|
433次组卷
|
7卷引用:新疆维吾尔自治区乌鲁木齐市第101中学2022-2023学年高二上学期期末数学试题
新疆维吾尔自治区乌鲁木齐市第101中学2022-2023学年高二上学期期末数学试题(已下线)2.3 圆与圆的位置关系(3)(已下线)模块三 专题5 大题分类练(直线和圆的方程)基础夯实练 期末终极研习室(高二人教A版)(已下线)第二章 直线与圆的方程(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)第02讲 2.4圆的方程+2.5直线与圆,圆与圆的位置关系(3)(已下线)通关练11 圆的方程大题10考点精练(47题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)专题2.3 圆与圆的位置关系(2个考点六大题型)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)