题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011618-81717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011618-80159.png)
答案
解析
专题:计算题。
分析:连接OE、OD,根据AC、BC分别切圆O于E、D,得到∠OEC=∠ODC=∠C=90°,证出正方形OECD,设圆O的半径是r,证△ODB∽△AEO,得出
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011618-28540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-83184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-50240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-45752.png)
解答:解:C、连接OE、OD,
∵AC、BC分别切圆O于E、D,
∴∠OEC=∠ODC=∠C=90°,
∵OE=OD,
∴四边形OECD是正方形,
∴OE=EC=CD=OD,
设圆O的半径是r,
∵OE∥BC,∴∠AOE=∠B,
∵∠AEO=∠ODB,
∴△ODB∽△AEO,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011618-28540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-76286.png)
解得:r=
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-83184.png)
A、设圆的半径是x,圆切AC于E,切BC于D,且AB于F,如图(1)同样得到正方形OECD,AE=AF,BD=BF,则a﹣x+b﹣x=c,求出x=
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-55925.png)
B、设圆切AB于F,圆的半径是y,连接OF,如图(2),则△BCA∽△OFA,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-50240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011620-16028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011620-39632.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011620-29573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-83184.png)
D、求不出圆的半径等于
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011619-83184.png)
故选C.
点评:本题主要考查对正方形的性质和判定,切线的性质,全等三角形的性质和判定,三角形的内切圆与内心,解一元一次方程等知识点的理解和掌握,能根据这些性质求出圆的半径是解此题的关键.
核心考点
举一反三
于点E,则DE的长是 .
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011615-36274.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011611-88166.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011611-74696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011611-44634.gif)
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![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011607-79059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011607-35357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011607-79059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011607-26025.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011608-80949.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011607-26025.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011606-29790.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011608-34609.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011608-65846.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011608-27754.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011600-93818.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011601-16137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011601-14670.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011601-26485.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011601-97199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011601-16137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011602-29978.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011601-16137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108011602-95402.gif)
22.选修4-1:几何证明选讲
如图,已知点C在圆O直径BE的延长线上,CA切
圆O于A点,DC是∠ACB的平分线并交AE于点F、交
AB于D点,则∠ADF=?
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