题目内容
如图,
内接于⊙O,
,
是⊙O上与点
关于圆心
成中心对称的点,
是
边上一点,连结
.已知
,
,
是线段
上一动点,连结
并延长交四边形
的一边于点
,且满足
,则
的值为_______________.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809216544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809231754.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809247315.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809263309.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809278292.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809294289.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809294398.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809309635.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809341472.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809481436.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809497333.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809512377.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809528409.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809543526.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809559303.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809575515.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809606553.png)
1或![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809621420.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809621420.png)
试题分析:因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809216544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809653750.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809668550.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809684610.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809699838.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809715547.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809731602.png)
当R在DC上时,此时可知AP=BP=10,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809746665.png)
适用两次折射定理得出,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809762958.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823024809777740.png)
点评:解答本题的关键是熟练掌握判定两个三角形全等的一般方法:SSS、SAS、ASA、AAS、HL,注意:AAA、SSA不能判定两个三角形全等,判定两个三角形全等时,必须有边的参与,若有两边一角对应相等时,角必须是两边的夹角.
![](http://thumb.zyjl.cn/images/loading.gif)
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