1 . 已知圆
的方程为
,直线
的方程为
,点
在直线
上,过点
作圆
的切线PA,PB,切点为A,B.四边形PAMB面积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f68c1991d753ba6b581a6872af26a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
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2 . 由直线
上的点
向圆
引切线
(
为切点),则线段
的最小长度为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23fc11a3a7592c68b20f93bdde2ed3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0d2f324341f7bc3186a5952ec97710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583183429b6b31aa9742eefc67d3181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d583183429b6b31aa9742eefc67d3181.png)
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2022-06-01更新
|
1705次组卷
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4卷引用:天津市静海区第一中学2021-2022学年高三上学期第四次阶段检测数学试题
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3 . 已知圆
的方程为
,点
是直线
上的一个动点,过点
作圆
的两条切线
、
,
、
为切点,则四边形
的面积的最小值为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044cfca7b534fa44075ded7f1a6aa038.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/d2be49c37e30a3ced0364c3e74d8c687.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/283b0cef5d644b8dceb910ce2c76f21c.png)
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2022-03-31更新
|
880次组卷
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10卷引用:天津市第九十五中学益中学校2021-2022学年高二上学期期中数学试题
天津市第九十五中学益中学校2021-2022学年高二上学期期中数学试题重庆市清华中学2021-2022学年高二上学期第二次月考数学试题(已下线)数学-2022年高考押题预测卷03(天津卷)(已下线)第12讲 直线与圆、圆与圆的位置关系(1)(已下线)2.2 直线与圆的位置关系(重点)(已下线)第2章 圆与方程(A卷·知识通关练)(1)天津市西青区第九十五中学益中学校2022-2023学年高二上学期期中阶段性检测数学试题甘肃省庆阳市宁县第二中学2022-2023学年高二上学期期末数学试题(已下线)重难点突破01 圆中的范围与最值问题(八大题型)甘肃省天水市第一中学2022-2023学年高二上学期1月期末考试数学试题
4 . 过直线
上任意点
作圆
的两条切线,切点分别为
,当切线长最小时,切线长为_________ ;同时
的面积为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33400b08941f4f9c0ed12b0e0cdff822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f25834d8218c53cb975c2a2fe7442a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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5 . 已知点
在圆
上,点
,
,有下列四个命题:
①点
到直线
的距离小于10;
②点
到直线
的距离大于2;
③当
最小时,
;
④当
最大时,
.
其中正确命题有________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924325c597b32a26f73add89f26114c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ba0cb4606d4847f791ada94045b990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe6f63d487d675e627bcb0a337b482d.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bebb16c0ffc99a945619ae0986cadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e1b79ad0713b7c30532e0a6d1370d6b.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bebb16c0ffc99a945619ae0986cadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f54dc4c9506a29296e1838a2dc0dae1.png)
其中正确命题有
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2022-05-03更新
|
224次组卷
|
3卷引用:贵州省黔东南州2020-2021学年高一下学期期末数学试题
贵州省黔东南州2020-2021学年高一下学期期末数学试题四川省凉山州会东县和文中学2022-2023学年高二上学期10月月考数学试题(已下线)2.5.1 直线与圆的位置关系【第三课】“上好三节课,做好三套题“高中数学素养晋级之路
名校
6 . 由直线
上的点P向圆C:
引切线
为切点
,当PT的长最小时,点P的坐标是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e127daadf14bb6aaf557b717eb27ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0572fd3f1b84128a18848a77c5ea9367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6b0d8f080f312b69d9ce7bfabcb565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ef244e9cd295656496929fbb46a9a5.png)
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7 . 过直线
上的动点
作圆
的切线,切点为
,则切线长
的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22950d09fef2d5a5433af09a416c8db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea17d831aa1206c699d66811a763236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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解题方法
8 . 点P是直线
上的动点,直线
与圆
分别相切于A,B两点,则当点 P的坐标为___________ 时, 切线段
的长度最短;四边形
面积的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d04eea839f7af2eadf4ed40020cdbee0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885fd9599ff0dbff75549d83d98c4c95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9597021d2b848b7f70c3f7b9e1da94a3.png)
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2022-02-11更新
|
396次组卷
|
4卷引用:重庆第二外国语学校2021-2022学年高二上学期期中数学试题
2022高三·江苏·专题练习
9 . 已知圆
,直线
,若直线与
轴交于点
,过直线
上一点
作圆
的切线,切点为
,若
,则点P的轨迹方程是____________ ;
的取值范围 是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e9c784624052cedf6b14e45099497b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc382157318685ce72b496ad621aeb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3512c910c7aa7fc2e133de847f6306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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10 . 过点
作圆
的切线,则点
到切点的距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc8057b074ab72aac23e47bd957c2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ab11ba6b230c4309e1b899eb58daae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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