题目
题型:不详难度:来源:
如图,已知:C是以AB为直径
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052830-25294.jpg)
CH⊥AB于点H,直线AC与过B点的切线相交于
点D,E为CH中点,连接AE并延长交BD于点F,
直线CF交直线AB于点G.
(Ⅰ)求证:F是BD的中点;
(Ⅱ)求证:CG是⊙O的切线.
答案
解析
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052831-99866.gif)
(Ⅱ)∵AB是直径,∴∠ACB=90°∴∠BCF=∠CBF=90°-∠CBA=∠CAB=∠ACO
∴∠OCF=90°,∴CG是⊙O的切线……………………………………………(10分)
(说明:也可证明△OCF≌△OBF(从略,仿上述评分标准给分))
点评:本题考查相似三角形判断及其性质,圆的切线的判断,属于容易题。
核心考点
试题【(选修4-1 几何证明选讲)如图,已知:C是以AB为直径的半圆O上一点,CH⊥AB于点H,直线AC与过B点的切线相交于点D,E为CH中点,连接AE并延长交BD于】;主要考察你对圆的方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052820-11392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052820-41284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052821-82638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052821-79613.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052821-23905.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052820-41284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052821-12989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052820-41284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052822-64026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052822-91537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052820-41284.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052822-18518.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-19631.jpg)
如图,圆O的直径
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-35535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-17947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-43337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-17947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-38278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-38278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-38278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052815-23649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052807-54344.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052807-14484.gif)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052758-82928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052758-76218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052758-73246.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052758-56928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052759-55091.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052759-73550.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052759-31289.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052759-22640.gif)
(Ⅰ)试判断四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052759-31289.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052759-22640.gif)
(Ⅱ)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052759-63875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052800-41451.gif)
的最大值及对应的
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052800-59177.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052800-53392.gif)
(Ⅲ)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052800-92683.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052801-36590.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052801-87309.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052801-66694.gif)
如图,
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052744-33577.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052744-29005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-19060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-96988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-54835.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-30244.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-38275.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-19060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-74558.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-23045.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052744-33577.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052744-29005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052746-70883.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052746-80494.gif)
(Ⅰ)建立适当坐标系,求铁路线所在圆弧的方程;
(Ⅱ)若该城市的某中学拟在点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-19060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052745-19060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052746-70883.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023052746-68531.gif)
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