题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052002-44023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052002-86041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052002-72171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052002-58353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052003-55547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052003-55510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052003-31657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052003-71989.png)
A.![]() | B.![]() | C.![]() | D.![]() |
答案
解析
试题分析:先作PO⊥平面ABC,垂足为O,根据条件可证得点O为三角形ABC的外心,从而确定点O为AC的中点,然后证明BO是面PAC的垂线,从而得到∠BEO为BE与平面PAC所成的角,在直角三角形BOE中求解即可。
解: 如图:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052005-84944.png)
作PO⊥平面ABC,垂足为O,则∠POA=∠POB=∠POC=90°,,而PA=PB=PC,PO是△POA、△POB、△POC的公共边,∴△POA≌△POB≌△POC,∴AO=BO=CO,则点O为三角形ABC的外心,∵△ABC是等腰直角三角形,∠ABC=90°,∴点O为AC的中点,则BO⊥AC,而PO⊥BO,PO∩AC=O,∴BO⊥平面PAC,连接OE,∴∠BEO为BE与平面PAC所成的角,∵点O为AC的中点,E为PC中点,PA=PB=PC=AC=1,ABC是等腰直角三角形,∠ABC=90°,∴OE为中位线,且OE=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052005-32333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022052005-32333.png)
点评:本题主要考查了三角形的外心的概念,以及直线与平面所成角和三角形全等等有关知识,同时考查了推理能力,属于中档题.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051945-22304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051945-44956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051945-56482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051945-85736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051946-97387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051946-37835.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051946-98384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051946-63785.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051947-73390.png)
(3)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051947-60494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051946-63785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051935-63505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051935-67186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051936-81887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051936-34788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051936-37809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051936-20694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051936-55669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051936-20694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051937-88125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051937-64891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051937-41134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051937-38088.jpg)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051924-45836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051924-79128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051924-73037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051924-70289.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051911-31851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051911-74777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051911-55099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051911-19616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051911-20275.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051912-65846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022051912-56548.png)
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