题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005718-50611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005718-12606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005718-49270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005718-11774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005718-66057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005719-88812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005719-61207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005719-76942.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005720-18197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005720-40180.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005718-66057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005720-83871.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005720-19979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005720-47096.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005721-67482.png)
解析
解(1)取BD的中点O,连接OE.
∵BE平分∠ABC,∴∠CBE=∠OBE.又∵OB=OE,∴∠OBE=∠BEO,
∴∠CBE=∠BEO,∴BC∥OE.………………3分
∵∠C=90°,∴OE⊥AC,∴AC是△BDE的外接圆的切线. 5分
(2)设⊙O的半径为r,则在△AOE中,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005721-43240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005721-29751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005721-42708.png)
∴OA=2OE,∴∠A=30°,∠AOE=60°.∴∠CBE=∠OBE=30°.
∴EC=
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005721-67482.png)
核心考点
举一反三
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005708-14941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005709-47904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005709-67483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005709-47904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005709-70536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005709-36887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005709-12603.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005710-29028.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005710-19928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005708-14941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005710-66459.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005701-35029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005701-34084.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005655-40320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005656-90168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005656-61887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005656-29268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005657-27813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005656-90168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005657-21721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005657-46359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005657-94631.png)
如图,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005651-67309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005651-66652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005651-34779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005651-66652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005652-74997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005652-33782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005651-66652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005652-79782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005652-36191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005653-31642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005651-34779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005653-96478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005651-66652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005653-72828.png)
如图,⊙O内切△ABC的边于D、E、F,AB=AC,连接AD交⊙O于点H,直线HF交BC的延长线于点G.
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005642-35100.png)
⑴证明:圆心O在直线AD上;
⑵证明:点C是线段GD的中点.
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