题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234718-58433.png)
小题1:BE=BC
小题2:AE2=AC·EC
答案
小题1:见解析
小题2:见解析
解析
因为∠CEB=∠A+∠EBA所以∠CEB=∠ABC由因为AB=AC,即∠ABC=∠C所以∠CEB=∠C,即BE=BC
(2)由(1)得,在△BCE中,∠C=72°,∠CBE=36°,
∴∠BEC=∠C=72°,
∴BC=BE=AE.(4分)
在△ABC与△BEC中,∠CBE=∠A,∠C=∠C,
∴△ABC∽△BEC.(6分)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234719-26499.png)
即BC2=AC•EC.(7分)
故AE2=AC•EC
核心考点
试题【如图,在△ABC中,AB=AC,∠A=36°,线段AB的垂直平分线交AB于D,交AC于E,连接BE求证:小题1:BE=BC小题2:AE2=AC·EC】;主要考察你对相似图形等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234715-70648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234703-97397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234704-78446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234704-47599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234704-93696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234704-93864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234705-49400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234705-76554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234704-93696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234705-84683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234705-32571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234706-53149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234706-95996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234706-71540.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234706-37683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234704-47599.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234707-55348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234707-14226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234705-76554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234657-52893.png)
(1)如图1,当∠C=45°时,请写出图中一对相等的线段;_________________
(2)如图2,若BD=2,BA=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234658-86766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234653-90145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234654-69530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234648-26823.png)
(1)求证:PB是⊙O的切线;
(2)求证: AQ·PQ= OQ·BQ;
(3)设∠AOQ=
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234648-59106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234648-59106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102234649-47297.png)
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