题目
题型:不详难度:来源:
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-41467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-98906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-16494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-48001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-77095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-44656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-64951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-89127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-46826.png)
(1)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-82576.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-65522.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-11044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-41467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-98906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-77629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-64951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-89127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005142-23313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005142-23696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005142-99904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005143-90524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005143-93056.png)
解析
试题分析:(1)证明:连结
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-11044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005143-44785.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-41467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-98906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-77629.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-64951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-89127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005142-23313.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005142-23696.png)
由圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-77095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-44656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005142-99904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005143-90524.png)
(2)解:由(1)得
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005143-14293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005144-86847.png)
由(1)得
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-77629.png)
由圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-77095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-44656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005144-51170.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005144-76979.png)
点评:证明四点共圆需证四边形对角互补
核心考点
举一反三
如图,AB是⊙O的直径 ,AC是弦 ,∠BAC的平分线AD交⊙O于点D,DE⊥AC,交AC的延长线于点E.OE交AD于点F.
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005133-13797.png)
(1)求证:DE是⊙O的切线;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005133-52974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005133-37378.png)
如图,A,B,C,D四点在同一圆上,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005123-63950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005123-88373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005123-97463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005124-95318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005124-84430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005124-12323.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005124-30576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005125-92381.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005125-19638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005125-60643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005114-59437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005115-30516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005115-82973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005115-46850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005115-64038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005116-78563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005116-28191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005116-36205.png)
如图,△ABC是⊙O的内接三角形,PA是⊙O的切线,PB交AC于点E,交⊙O于点D,若PE=PA,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005111-93357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005112-24440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005106-84155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005106-18847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005106-33328.png)
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