解题方法
1 . 已知圆C:
与直线l:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45af4fa45634408f1cb2e44aeda628a.png)
(1)证明:直线
和圆
恒有两个交点;
(2)若直线
和圆
交于
两点,求
的最小值及此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a32c27759b330c663dca1db376d102e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45af4fa45634408f1cb2e44aeda628a.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-11-22更新
|
176次组卷
|
3卷引用:河南省开封市立洋外国语学校2022-2023学年高二上学期第二次月考数学试题
2 . 如图,在四棱锥
中,底面
是边长为2的正方形,
是等边三角形,平面
平面
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/66248ef6-8b0b-4516-8c9c-9ffe521b757e.png?resizew=204)
(1)证明:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bf40f6235d0231481c2598e2ba977b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47891397990336f55f96bd66d367758b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/66248ef6-8b0b-4516-8c9c-9ffe521b757e.png?resizew=204)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2022-11-21更新
|
532次组卷
|
4卷引用:河南省驻马店经济开发区高级中学等2022-2023学年高三上学期11月联考文科数学试题
河南省驻马店经济开发区高级中学等2022-2023学年高三上学期11月联考文科数学试题贵州省部分学校2023届高三上学期11月联考数学(文)试题(已下线)第30讲 面面垂直的判定定理及性质2种题型(已下线)8.6.3 平面与平面垂直(精练)
名校
解题方法
3 . 如图1,四边形
是梯形,
是
的中点,将
沿
折起至
,如图2,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/2022/8/25/3051997355786240/3052662834151424/STEM/11b16ef4ffa04da5840a560dcd5860b6.png?resizew=170)
![](https://img.xkw.com/dksih/QBM/2022/8/25/3051997355786240/3052662834151424/STEM/d1324d2e5c26489b941c7fdb7030c258.png?resizew=165)
(1)若
是
的中点,求证:平面
平面
;
(2)若
,平面
与平面
夹角的余弦值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2768b54752183b24f77a6a0bd5a542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f9fba8a4098c1a0515286eb8d616dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee9bc57f1a415b5790b5b40854c832e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://img.xkw.com/dksih/QBM/2022/8/25/3051997355786240/3052662834151424/STEM/11b16ef4ffa04da5840a560dcd5860b6.png?resizew=170)
![](https://img.xkw.com/dksih/QBM/2022/8/25/3051997355786240/3052662834151424/STEM/d1324d2e5c26489b941c7fdb7030c258.png?resizew=165)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675e62b42d5693606536cd993e8e74e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719103f93166bab4828257608e641a9a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbccb1ba0e436c5a3296955e8dd38853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b559200a2caa639355f7bc2ed8d37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe67036b4671b5d2a5c55b48c4d3bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2012a47fba3643fec7aea1f3fc41eac.png)
您最近一年使用:0次
2022-08-26更新
|
1200次组卷
|
6卷引用:河南省濮阳市南乐县第一高级中学2022-2023学年高二上学期第二次月考理科数学重点班试题
解题方法
4 . 在正方体
中,
为
的中点,
为棱
上一点,平面
交棱
于点
,交棱
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/82065d21-1cd4-4f60-9aa7-499d95ec1552.png?resizew=146)
(1)若
,求
;
(2)若
,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2906d4142e9715cdac924510d8c44f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/82065d21-1cd4-4f60-9aa7-499d95ec1552.png?resizew=146)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5cd31e96c7b52a18074993829b18c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddb339df743a4f0347823beee5516b6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f500345f1879c259ce50539272d85e42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4250bb6bc8aa91b3f84538f2c7581fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-09-30更新
|
238次组卷
|
3卷引用:河南省部分名校2022-2023学年高二上学期9月联考数学试题(北师大版)
河南省部分名校2022-2023学年高二上学期9月联考数学试题(北师大版)(已下线)8.5.2直线与平面平行(精练)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)山西省朔州市怀仁市第九中学高中部2023-2024学年高二上学期期中数学试题
名校
解题方法
5 . 如图,在长方体ABCD-A1B1C1D1中,E,F分别为BC,CC1的中点,AB=AD=2,AA1=3.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/1587974a-38f7-49a0-8c58-8cb2b644afcb.png?resizew=173)
(1)证明:EF∥平面A1ADD1;
(2)求直线AC1与平面A1ADD1所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/1587974a-38f7-49a0-8c58-8cb2b644afcb.png?resizew=173)
(1)证明:EF∥平面A1ADD1;
(2)求直线AC1与平面A1ADD1所成角的正弦值.
您最近一年使用:0次
2022-09-20更新
|
641次组卷
|
7卷引用:河南省安阳市第一中学2022-2023学年高二上学期第一次阶段考试文科数学试题
河南省安阳市第一中学2022-2023学年高二上学期第一次阶段考试文科数学试题江苏省南通市如东高级中学2019-2020学年高一下学期期中数学试题江苏省南通市如东县2019-2020学年高一下学期期中数学试题(已下线)第50讲 用综合法求角与距离(已下线)第52讲 空间向量在立体几何中的运用(已下线)8.6.2 空间角与空间距离(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)8.6.2直线与平面垂直的判定定理(第1课时)(精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
6 . 如图,所有棱长均相等的正三棱柱
中,E,F分别是棱BC,
上的点,记EF与
所成的角为
,EF与平面ABC所成的角为
,二面角
的平面角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/7e31e505-a44d-4c3b-ad26-1e1b6146f2c7.png?resizew=186)
(1)当
时,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
,试确定点F的位置;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b6797e834bb430abf574c2f2b3c107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/7e31e505-a44d-4c3b-ad26-1e1b6146f2c7.png?resizew=186)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104cacf19f1897c6c86d24c5fe8cb991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e13f82da9187b78bf5aa6839f105da1.png)
您最近一年使用:0次
解题方法
7 . 如图,已知
是正三角形,
、
都垂直于平面
,且
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/12/3020865902657536/3024061129170944/STEM/153f37ea158e410f9f867a5ac46b54d9.png?resizew=127)
(1)求证:
平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84427d1060a50556a161c8d7a1b5f4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/2022/7/12/3020865902657536/3024061129170944/STEM/153f37ea158e410f9f867a5ac46b54d9.png?resizew=127)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b9c913de19bd5d9a0a67d88ff1371f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
您最近一年使用:0次
解题方法
8 . 已知三棱柱
中,
,
,
平面ABC,E为AB的中点,
为
上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/a5daaa2b-7be0-46a9-8bf7-48cd79d44fee.png?resizew=190)
(1)求证:
;
(2)当
为
的中点时,求三棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa345e314208fcb6b3b29cb8130be32c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/a5daaa2b-7be0-46a9-8bf7-48cd79d44fee.png?resizew=190)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd5c41c921836b50f8e18abfdc5df3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
您最近一年使用:0次
名校
解题方法
9 . 在三棱锥
中,
,
,
、
分别是棱
、
的中点.
;
(2)线段
上是否存在点
,使得
平面
?若存在,指出点
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbbe7f48676298f2ee0cb1901992eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
2022-09-29更新
|
962次组卷
|
9卷引用:河南省南阳市第一中学校2023届高三上学期第三次阶段性测试文科数学试题
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名校
解题方法
10 . 如图,在三棱柱
中,侧面
底面
,
,
,且
,
为
中点.
![](https://img.xkw.com/dksih/QBM/2022/8/25/3052106803642368/3058231501807616/STEM/fcc2dcadb93e4ee5970fa6e1bd364e7a.png?resizew=288)
(1)求证
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb88c278e18d776f165bc571031071d8.png)
(2)在
上是否存在一点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
平面
,若不存在,说明理由;若存在,确定点E的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58bd6407cc044990cc765df9e710369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2022/8/25/3052106803642368/3058231501807616/STEM/fcc2dcadb93e4ee5970fa6e1bd364e7a.png?resizew=288)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb88c278e18d776f165bc571031071d8.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
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