(1)∵四边形DCBE为平行四边形 ∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658506445.gif)
∵DC
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658568108.gif)
平面ABC ∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658584260.gif)
平面ABC
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658600397.gif)
为AE与平面ABC所成的角,即
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658600397.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658241200.gif)
--------------------2分
在Rt△ABE中,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658678693.gif)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658194276.gif)
得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658740325.gif)
------------3分
∵AB是圆O的直径 ∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658756321.gif)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658771657.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082313165878773.gif)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658802739.gif)
----------------------------------------4分
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658818788.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658849520.gif)
------------------5分
(2)在CD上存在点
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658865327.gif)
,使得MO
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658896184.gif)
平面
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658444275.gif)
,该点
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131658865327.gif)
为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659021246.gif)
的中点. ---10分
证明如下:
如图,取
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659224241.gif)
的中点
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659239211.gif)
,连MO、MN、NO,
∵M、N、O分别为CD、BE、AB的中点,
∴.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659255470.gif)
----------------------------------------------11分
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659286267.gif)
平面ADE,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659302414.gif)
平面ADE,
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659317590.gif)
------------------------------------------------------12分
同理可得NO//平面ADE.
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659333559.gif)
,∴平面MNO//平面ADE.--------------------13分
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823131659348388.gif)
平面MNO,∴MO//平面ADE. -------------14分(其它证法请参照给分)