题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030230-36325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030230-86037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030231-56591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030231-93710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030231-10323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030231-90740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030232-20552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030232-13618.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030232-27837.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030232-10761.png)
答案
解析
试题分析:本题主要以圆为几何背景考查线线相等的证明及相似三角形的证明,可以运用角之间的关系证明等腰,运用相似三角形的基本证明方法求证.第一问,转化角,证明
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030233-57982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030232-27837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030233-68450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030233-37254.png)
试题解析:(1)连结
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030233-62470.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030233-77389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030234-20425.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030230-36325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030230-86037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030231-56591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030234-35396.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030234-50773.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030234-40464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030234-47187.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030235-92566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030233-57982.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030232-27837.png)
(2)由(1)知,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030235-77633.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030235-50228.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030233-68450.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030235-26666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030233-37254.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030223-51095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030223-69884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030224-97074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030224-39973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030223-69884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030224-77471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030224-27019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030223-69884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030225-54680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030225-14217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030225-24117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030216-19172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030216-55423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030217-63052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030217-18063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030216-55423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030217-93645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030217-56417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030217-76748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030218-77708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030218-80798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030218-20411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030218-43565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030219-29647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030208-30866.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030208-42439.png)
(Ⅱ)若BC、PD相交于点M,则
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030208-13410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030157-84063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030157-78262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030158-92208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030158-29412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030158-85799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030158-62653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030158-45789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030159-58835.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030159-67786.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030159-52770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030159-88722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023030148-93365.png)
(Ⅰ)求证:BE=2AD;
(Ⅱ)当AC=1,EC=2时,求AD的长.
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