题目
题型:不详难度:来源:
如图,已知C、F是以AB为直径的半圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231308-10718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231308-48585.png)
(Ⅰ)证明:CD为圆O的切线;
(Ⅱ)若AD=3,AB=4,求AC的长.
答案
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231308-20459.png)
解析
试题分析:(Ⅰ)证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231308-73402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231309-54262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231309-97676.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231309-27840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231309-94783.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231310-78690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231310-41499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231310-92680.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231310-31518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231310-48549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231311-31090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231308-10718.png)
(Ⅱ)解:连接
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231311-45327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231311-27879.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231311-35730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231312-86064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231312-51885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231312-23126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231312-25928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231308-20459.png)
点评:对于线段的长度的求解,一般运用相似的思想来得到。或者借助于切线长定理等等的知识得到关系式来得到。
核心考点
试题【(本题满分10分)如图,已知C、F是以AB为直径的半圆上的两点,且CF=CB,过C作CD^AF交AF的延长线与点D.(Ⅰ)证明:CD为圆O的切线;(Ⅱ)若AD=】;主要考察你对点到直线的距离等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231302-45370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231302-56968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231302-32128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231302-51599.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231257-98546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231257-22698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231257-91878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231257-49280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231250-66952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231250-16591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231250-67798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231251-89967.png)
(1)求证:直线和圆相交
(2)当圆截直线所得弦最长时,求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231251-31718.png)
(3)直线将圆分成两个弓形,当弓形面积之差最大时,求直线方程
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231246-56320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231232-56078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231233-70822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231233-16949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231233-38364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231233-94253.jpg)
(Ⅰ)求圆心M在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231233-52769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231233-16949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231234-47177.png)
(Ⅱ)在(Ⅰ)的条件下;若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231234-24319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231234-92576.png)
求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022231234-24559.png)
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