题目
题型:不详难度:来源:
(选修4-1) 如图,在
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005827-25565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005827-65570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005827-87703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005827-94712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005828-95225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005828-51119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005828-18726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005828-27085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005828-46815.png)
(I)求证:直线
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005828-81390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005827-94712.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-20573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005827-94712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-53797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-70079.png)
答案
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-92582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-89521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-49417.png)
再由等腰
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-44154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005830-72142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005830-35589.png)
(II) 证明本题的关键是证明
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005830-37283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005830-89290.png)
证明:(Ⅰ)连接
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-92582.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005830-86133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-89521.png)
则有在等腰
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005831-74560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-49417.png)
在等腰
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-44154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005830-72142.png)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005831-44640.png)
即直线
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005828-81390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005827-94712.png)
(Ⅱ)连接
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005831-42013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005831-13138.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005832-66868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005832-81112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005830-37283.png)
因此得到
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005829-70079.png)
核心考点
试题【(本小题满分10分).(选修4-1) 如图,在中,,以为直径的圆交于点,设为的中点. (I)求证:直线为圆的切线;(Ⅱ)设交圆于点,求证: 】;主要考察你对圆锥曲线性质探讨等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005820-43293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005814-59441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005815-73994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005815-70895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005815-92594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005815-30425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005816-18086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005816-85577.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005816-97017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005810-28282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005810-13064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005810-62728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005810-20108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005810-13064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005811-20899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005811-89902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005811-32242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005810-13064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005811-85109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005805-16217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005806-30159.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005806-14537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005806-82910.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005801-60846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005801-81622.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005801-95165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005801-72568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005801-27982.png)
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