名校
解题方法
1 . 如图,已知在四面体
中,
,
,
.
、
分别为
、
中点.
为
、
的公垂线;
(2)求空间内任一点
到四面体
四个顶点距离和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e096f87473d0b6b6d531ba22e5a7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c838e9a018189b92b1a56d57aa26389e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf7c885153243a3f763c4c8e6268247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)求空间内任一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,棱长为2的正方体
中,E、F分别是棱AB,AD的中点,G为棱
上的动点.
(1)是否存在一点G,使得
面
?若存在,指出点G位置,并证明你的结论,若不存在,说明理由;
(2)若直线EG与平面
所成的角为
,求三棱锥
的体积;
(3)求三棱锥
的外接球半径的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
(1)是否存在一点G,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd597851c0db4e4de4769e10e09383b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(2)若直线EG与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d58bf185026e4f6b568f1d5677074b.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493d7a008d5cc07e719e2e58b07a3abc.png)
您最近一年使用:0次
3 . 图1是由正方形
组成的一个等腰梯形,其中
,将
、
分别沿
折起使得E与F重合,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/96241205-5ee2-45fe-a504-beb19971deba.png?resizew=315)
(1)设平面
平面
,证明:
;
(2)若二面角
的余弦值为
,求
长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f0391c01548b0b5968f5b72cdd203a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df7626240940eb340420a605e95aeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/96241205-5ee2-45fe-a504-beb19971deba.png?resizew=315)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca0832e094d5c05ec13c38ae556b3f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c0566d4ccf791d639c7823398941d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56adc934c9ad3cb261c5cbdc346b9631.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445b51117626fbd3373e32acc514c64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
2021-04-16更新
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1064次组卷
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7卷引用:四川省泸县第四中学2022-2023学年高二上学期期末考试数学(理)试题