题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020505-15697.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020506-40795.png)
解析
试题分析:连接OC,由M为CD的中点可得EM⊥CD,根据垂径定理可得CM=MD=2,由EM=6可得OM=6-R,在Rt△CMO中,根据勾股定理即可列方程求解.
连接OC
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020506-19577.png)
∵EM过圆心O,M为CD的中点
∴EM⊥CD,OE=OC=R
由垂径定理可得:CM=MD=2
∵EM=6
∴OM=6-R
在Rt△CMO中,由勾股定理可得:
CO2=CM2+MO2
即R2=22+(6-R)2
解得R=
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020506-40795.png)
点评:解题的关键是熟练掌握垂径定理:垂直于弦的直径平分弦,且平分弦所对的弧.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020500-48488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020500-69347.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105020456-74482.jpg)
A.![]() | B.![]() | C.![]() | D.![]() |
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相切, ⊙
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(
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如图甲, 求证:
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甲 乙
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