名校
1 . 如图,在
中,
,
,
为
的外心,
平面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/a7bf8dcc-e15c-4c4e-a87d-a181e025bb0d.png?resizew=160)
(1)求证:
平面
;并计算
与平面
之间的距离;
(2)设平面
面
,若点
在线段
(不含端点)上运动,当直线
与平面
所成角取最大值时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac34466d49ce1fe5dd29d02f02e5cd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f46d6df1be75b608e537baf05473c2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/a7bf8dcc-e15c-4c4e-a87d-a181e025bb0d.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed56139dcd641263e11f27e4d8ed56c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4838fcc4413794bc2559e634d7be94de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e61111c1e9b98b79615f75540175c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b478ba337ecb3c256e451d10eeff5c1.png)
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2021-10-21更新
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5卷引用:山西省运城市高中联合体2022届高三下学期第四次模拟数学(理)试题