1 . 如图,已知四边形
为等腰梯形,
,
,四边形
为矩形,点
,
分别是线段
,
的中点,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/33fbce59-ed15-40c5-8c4c-e14b738c488b.png?resizew=204)
(1)探究:是否存在点
,使得平面
平面
?并证明;
(2)若
,线段
在平面
内的投影与线段
重合,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b6d19fedaf8488f9637cd64efbca83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a406f24b5131eb7da9127750319e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/33fbce59-ed15-40c5-8c4c-e14b738c488b.png?resizew=204)
(1)探究:是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9353ffd1091c2edf5ad40df632817f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ac7cf883a6e586d06e3f33875bd95b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd5237ca28310ba21f98ced3883c6c23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3465fa12d8a88ae29d90c00504c2a979.png)
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2 . 如图,在四棱锥P-ABCD中,平面PBC⊥平面ABCD.∠BDC=90°,BC=1,BP=
,PC=2.
![](https://img.xkw.com/dksih/QBM/2020/11/20/2597254318399488/2598528165011456/STEM/87c807bc-5c7a-4bf2-aa06-88a499425c12.png)
(1)求证:CD⊥平面PBD;
(2)若BD与底面PBC所成的角为
,求二面角B-PC-D的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef812f839622326a7d7027cc806aaeb.png)
![](https://img.xkw.com/dksih/QBM/2020/11/20/2597254318399488/2598528165011456/STEM/87c807bc-5c7a-4bf2-aa06-88a499425c12.png)
(1)求证:CD⊥平面PBD;
(2)若BD与底面PBC所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9303b41310b6bf2a5fe9b66dfcd7fcb5.png)
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3 . 一条光线从点
射出,经y轴反射后与圆
相交,则入射光线所在直线的斜率的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0924ff22fff9f5639feb0ceeece80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a353d1a988596880c0a48c2303d20c2c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7卷引用:安徽省蚌埠市怀远县第一中学2020-2021学年高二上学期第三次月考文科数学试题
安徽省蚌埠市怀远县第一中学2020-2021学年高二上学期第三次月考文科数学试题(已下线)第36练 直线与圆的位置关系-2021年高考数学(文)一轮复习小题必刷(已下线)考点03+圆及其方程-2020-2021学年【补习教材·寒假作业】高二数学(人教B版2019)(已下线)专题11 直线与圆-备战2021年高考数学(理)二轮复习题型专练?(通用版)江西省五市九校协作体2023届高三第二次联考数学(文)试题(已下线)2.5.1 直线与圆的位置关系(第2课时)(分层作业)(3种题型分类基础练+能力提升练)-【上好课】高二数学同步备课系列(人教A版2019选择性必修第一册)山东省威海市乳山市银滩高级中学2023-2024学年高二上学期10月月考数学试题
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4 . 如图所示,平面ABEF⊥平面ABC,四边形ABEF是矩形,AB=2,AF=
,△ABC是以A为直角的等腰直角三角形,点P是线段BF上的一点,PF=3.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/57a2d8c3-fd83-4f6a-96c5-5c0dd3f8927d.png?resizew=188)
(1)证明:AC⊥BF;
(2)求直线BC与平面PAC所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/57a2d8c3-fd83-4f6a-96c5-5c0dd3f8927d.png?resizew=188)
(1)证明:AC⊥BF;
(2)求直线BC与平面PAC所成角的正切值.
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3卷引用:浙江省金华市东阳中学2020-2021学年高三上学期期中数学试题
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5 . 圆
的圆心坐标和半径长分别是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84206d21aa3ed77b34939ccc0252838.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:四川省乐山市十校2020-2021学年高二上学期期中联考数学(文)试题
名校
解题方法
6 . 如图,圆柱的轴截面
是正方形,点
是底面圆周上异于
的一点,
,
是垂足.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/0944bc73-af3d-4f0b-8a26-95b1ca887fa2.png?resizew=148)
(1)证明:
;
(2)若
,当三棱锥
体积最大时,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876bb8ce0ca53475fa091ffd18bdc94a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/0944bc73-af3d-4f0b-8a26-95b1ca887fa2.png?resizew=148)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e3d90003d6940c8e9e90916172ba97.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2daa808ca8c95f282dae5e1d578cb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
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5卷引用:云南师范大学附属中学呈贡校区2020—2021学年高二上学期第一学段模块考试(期中考试)试题
名校
解题方法
7 . 如图所示,正方体
的棱长为1,
分别是棱
的中点,过直线
的平面分别与棱
交于
,设
,则正确的说法是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/375ed89d-b2e6-4ad1-82e9-b77e8ff5027d.png?resizew=185)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b1d726cf581f600890723a3cf6cdb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8db934d1174fb0f07abe18ac353b4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b2d1674d45273b146bef2fcfbdb2ec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/375ed89d-b2e6-4ad1-82e9-b77e8ff5027d.png?resizew=185)
A.四边形![]() |
B.若四边形![]() ![]() ![]() |
C.若四棱锥![]() ![]() ![]() |
D.若多面体![]() ![]() ![]() |
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3卷引用:广东省茂名市五校联盟2021届高三上学期第一次联考数学试题
广东省茂名市五校联盟2021届高三上学期第一次联考数学试题福建省厦门双十中学2021届高三12月月考数学试题(已下线)黄金卷04-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(山东高考专用)
20-21高三上·浙江·阶段练习
名校
解题方法
8 . 曲线
与直线
有两个交点,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b22ace7070514ef8059c02834fe29d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce5d8e50dfc56d555b10f38f34782848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:2021年1月浙江省普通高中学业水平考试数学仿真模拟试卷01
(已下线)2021年1月浙江省普通高中学业水平考试数学仿真模拟试卷01天津市实验中学2021-2022学年高二上学期期中数学试题湖北省黄冈市黄梅国际育才高级中学2022-2023学年高二上学期期中数学试题
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9 . 已知圆
,点
,其中
.
(1)若直线
与圆
相切,求直线
的方程;
(2)若在圆
上存在点
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbd54e4f836a12ecd1cf365dc24a7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0f03c1a636063c0bd1cb153de8711f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若在圆
![](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/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 如图,已知四棱锥
中,
平面
,
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/357b72c2-4d02-4409-ba34-bdcca31b9b71.png?resizew=148)
(Ⅰ)求证:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60bb2e3631f46fc8a24595efce01a92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a078495ba47076ccaa28b46f765d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a6fb3ab9f27db017de6f80074715b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3a6dcaf9f9e9a940b4a16f7ec2fc2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/357b72c2-4d02-4409-ba34-bdcca31b9b71.png?resizew=148)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
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4卷引用:浙江省湖州市三贤联盟2020-2021学年高二上学期期中联考数学试题
浙江省湖州市三贤联盟2020-2021学年高二上学期期中联考数学试题(已下线)【新东方】【2020】【高二上】【期中】【HD-LP365】【数学】(已下线)【新东方】杭州新东方高中数学试卷363江西省吉安县立中学2020-2021学年高二12月月考数学(理A)试题