题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031344-95288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031344-87961.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031344-44835.jpg)
(Ⅰ)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031344-23009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-19789.gif)
(Ⅱ)设AB=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-76489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031344-95288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031344-87961.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-22155.gif)
(i)当点C在圆周上运动时,求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-22155.gif)
(ii)记平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-55014.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031346-53535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031346-53107.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031346-50400.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-22155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031346-76569.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031346-52688.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-67722.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-76489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-87006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-19861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-76489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-87006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-32096.gif)
因为AB是圆O直径,所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-32096.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-87006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-33906.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031348-98409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031348-63274.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-32096.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-87006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-55014.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-19861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-19789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031344-23009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-19789.gif)
(Ⅱ)(i)设圆柱的底面半径为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031348-30588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031348-89048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031344-87961.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031349-44769.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031349-35312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031349-88850.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031349-30549.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031350-60270.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031350-11083.gif)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031350-58576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031350-42209.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-22155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031350-90738.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031350-11083.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031351-53865.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-22155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031346-52688.gif)
(ii)由(i)可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-22155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031351-53865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031351-30171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031351-35573.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-32096.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031347-87006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-55014.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031351-66875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031345-55014.gif)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031346-53535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031351-39960.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031352-12063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031352-79030.gif)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031352-84975.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031346-53535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031352-55599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031353-32137.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031353-35376.gif)
核心考点
试题【如图,圆柱内有一个三棱柱,三棱柱的底面为圆柱底面的内接三角形,且AB是圆O直径。(Ⅰ)证明:平面平面;(Ⅱ)设AB=,在圆柱内随机选取一点,记该点取自于三棱柱内】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031339-54164.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031339-34814.gif)
(II)求CC1到平面A1AB的距离;
(理)(III)求二面角A—A1B—C的大小
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031328-98451.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031328-86416.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031328-15464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031328-48308.gif)
四边形DCBE为平行四边形,DC
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031329-10366.gif)
(1)求三棱锥C-ABE的体积;
(2)证明:平面ACD
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031329-10366.gif)
(3)在CD上是否存在一点M,使得MO//平面ADE?证明你的结论.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031329-82530.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031324-56043.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031325-73796.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031325-56659.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031317-57250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031317-93418.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031318-67606.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031318-48886.gif)
① 四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031318-54438.gif)
② 四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031318-54438.gif)
③ 四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031318-54438.gif)
④ 四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031318-54438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031318-38494.gif)
以上结论正确的为 。(写出所有正确结论的编号)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031308-93051.jpg)
如图,在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031308-39077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031308-58930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031308-96166.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031308-80717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031308-96166.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031309-18614.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031309-40356.gif)
(1) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031309-26732.gif)
(2) 点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031309-12699.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031308-58930.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031309-36881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021031309-66362.gif)
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