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)
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2 . 设
是定义在
上的奇函数,且当
时,
单调递减,若
,则
的值( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc8f775c0c874c4ea920136a91db8f.png)
A.恒为负值 | B.恒等于零 |
C.恒为正值 | D.无法确定正负 |
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9卷引用:甘肃省兰州市第五十中学2022-2023学年高三上学期第一次模拟考试数学(文科)试题
甘肃省兰州市第五十中学2022-2023学年高三上学期第一次模拟考试数学(文科)试题四川省眉山市眉山中学2017-2018学年高一10月月考数学试题山西省应县第一中学校2018-2019学年高二下学期期末考试数学(理)试题(已下线)专题11.2 直接证明与间接证明(练)【文】-《2020年高考一轮复习讲练测》(已下线)专题12.2 直接证明与间接证明、数学归纳法(精练)-2021届高考数学(文)一轮复习讲练测(已下线)专题12.2 直接证明与间接证明 (精练)-2021届高考数学(文)一轮复习学与练(已下线)专题12.2 直接证明与间接证明、数学归纳法(精练)-2021年高考数学(理)一轮复习讲练测(已下线)专题12.2 直接证明与间接证明、数学归纳法 (精练)-2021年高考数学(理)一轮复习学与练重庆市蜀都中学2020-2021学年高二上学期11月月考数学试题
2018高三·全国·专题练习
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3 . 已知函数
,若方程
恰有三个实数根,则实数
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ee975cd32e42962d574dcc23daab5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe68aa8a21f26b6b9f6889369aa5905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2017届福建省宁德市高三第一次(3月)质量检查数学理试卷(已下线)2-8 函数与方程(高效训练)-2019版导学教程一轮复习数学(人教版)山西省应县第一中学校2018-2019学年高二下学期期末考试数学(理)试题
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4 . 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)
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5 . 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.
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6 . 如图所示,已知直线
的方程为
,⊙
,⊙
是相外切的等圆.且分别与坐标轴及线段
相切,
,则两圆半径![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
__________ (用常数
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f6e613ffa032e7e893daa1970d3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2bc7331e651f466890b46111b962e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/4c1689d5-6d77-40e0-b08d-9da2426bc4fc.png?resizew=171)
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7 . 如图,在圆内接四边形
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925091064176640/1927240651849728/STEM/650e0052-8337-4afc-aacd-d76868387aeb.png)
(1)求
的大小;
(2)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de006cef9e5efbcbf74229845804650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925091064176640/1927240651849728/STEM/650e0052-8337-4afc-aacd-d76868387aeb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df6d51738ac1bc8b9530ea4a55745c2.png)
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2卷引用:2018年陕西省咸阳市第二次模拟理数试题
2010·黑龙江哈尔滨·一模
8 . 选修4-1:几何证明选讲
如图,已知
点在⊙
直径的延长线上,
切⊙
于
点,
是
的平分线,且交
于
点,交
于
点.
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f064c53e1030482cada14b5002913cf0.png)
(1)求
的度数;
(2)若
,求
.
如图,已知
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c9b96029815b4fee956f1dd14b16c519.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c195da6c33724175ad833081f8b6c367.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/658f5ce6c1c24beb9ee7d0862af41c9a.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/c195da6c33724175ad833081f8b6c367.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/86e450de1d844ab085556f65f163d0bb.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/3b024db94d38400ab4778285d6a147ed.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/6636f6ff0f0e4d44b6f35a63393fc31d.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/babf31d6a39c44ffb64ca8294ab0d531.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/3f2d4c92974d4a60b3adeefacffd3664.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/4b016ec3d5b544bdbe4990ea634529a5.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/2140925fcb9a4e16937624eb1dfe90f1.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f064c53e1030482cada14b5002913cf0.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/0c51a0a5c8ab4cec8af8be1657b0c9b4.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/58bb7d54d6444190b394bbcc7be1aaeb.png)
![](https://img.xkw.com/dksih/QBM/2010/4/7/1569692868911104/1569693001334784/STEM/f394ef40aaa64bbf9bba63b22333024d.png)
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2016-12-03更新
|
811次组卷
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6卷引用:黑龙江省哈尔滨市第六中学2010届高三一模数学(理)试题
(已下线)黑龙江省哈尔滨市第六中学2010届高三一模数学(理)试题(已下线)黑龙江省哈尔滨市第六中学2010届高三一模数学(文)试题2015届黑龙江省哈尔滨六中高三下学期第三次模拟理科数学试卷2015届贵州省贵阳市普通高中高三上学期期末监测考试理科数学试卷2015届贵州省贵阳市普通高中高三上学期期末监测考试文科数学试卷2016届黑龙江省哈尔滨市六中高三上期末理科数学试卷
9 . 选修4-1:几何证明选讲.
如图,圆周角
的平分线与圆交于点
,过点
的切线与弦
的延长线交于点
,
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/9a4d7e72-02d8-4427-9ec6-78288d954c03.png?resizew=139)
(1)求证:
;
(2)若
四点共圆,且弧
与弧
相等,求
如图,圆周角
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/9f391813265344e3b84b0add71f8735f.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/53a2deb9e45d47c5a5d523e5f3e9affb.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/53a2deb9e45d47c5a5d523e5f3e9affb.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/42a37ba17bed44ec8b1695afe12d8473.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/e9a7fb85543b434eb8d641b18020d179.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/fdf7e0242d064d49996745aea9a3a32a.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/dafb54ea36c244d6b6cc375a417274fc.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/2baab2bea819401da1ece84a3558ff91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/9a4d7e72-02d8-4427-9ec6-78288d954c03.png?resizew=139)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/f134a28849784be185d26d443598825a.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/e08368f8215244b28f869c2170e623e4.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/42a37ba17bed44ec8b1695afe12d8473.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/dafb54ea36c244d6b6cc375a417274fc.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122327072768/1572122333241344/STEM/9f391813265344e3b84b0add71f8735f.png)
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2016-12-03更新
|
480次组卷
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6卷引用:2015届黑龙江省哈尔滨九中高三第三次高考模拟理科数学试卷
10 . 如图所示,
为以
为直径的圆
的切线,
为切点,
为圆周上一点,
,直线
交
的延长线于点
.
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/a4ce8c32f06244e1a15242a05c5f3c2d.png)
(1)求证:直线
是圆
的切线;
(2)若
,
,求线段
的长.
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/f4d399a4d95f4e4986bc69e8addecbcb.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/d900b01e8d754989b68e7e5da50ae09a.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/4796d7d1550545f5841f0c855f935413.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/1e63e56eea8e48aa93d8b128221a22d6.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/3fe9e2a5e7bd45349202edeae9b53e05.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/c9bded80d9854945bb7cc5c935b41258.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/e2ea61d9b5d34e7a804fb12b7f51d9e7.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/d900b01e8d754989b68e7e5da50ae09a.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/6d6708a57d764cb6ae1494818111cfb8.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/a4ce8c32f06244e1a15242a05c5f3c2d.png)
(1)求证:直线
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/e2ea61d9b5d34e7a804fb12b7f51d9e7.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/4796d7d1550545f5841f0c855f935413.png)
(2)若
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/6e6758e09a3a4ee9a9f59155b6f7a204.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/390d78d8afa94721bed123c9f813853f.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572684181446656/1572684187820032/STEM/04fd07e407c74c8d9b3865d9ef7e322a.png)
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