题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001824-92923.png)
求:(1)⊙O的半径;
(2)s1n∠BAP的值。
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001825-65985.png)
解析
试题分析:(1)由题可知,利用切割线定理即可;(2)根据弦切角定理可知s1n∠BAP=s1n∠ACB,然后求出AB、BC的比值即可.
试题解析:(Ⅰ)因为PA为⊙O的切线,所以
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001825-14369.png)
又由PA=10,PB=5,所以PC=20,BC=20-5=15 2分.
因为BC为⊙O的直径,所以⊙O的半径为7.5. 4分
(2)∵PA为⊙O的切线,∴∠ACB=∠PAB, 5分
又由∠P=∠P, ∴△PAB∽△PCA,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001825-22350.png)
设AB=k,AC="2k," ∵BC为⊙O的直径,
∴AB⊥AC∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001825-55245.png)
∴s1n∠BAP=s1n∠ACB=
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001826-72169.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001819-39885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001819-11709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001813-79441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001813-57200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001814-29808.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001806-64260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001806-50897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001806-12666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001807-79605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001807-30602.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001807-92923.jpg)
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![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001753-16371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001754-80001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001753-11550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001754-31760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001753-16371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001754-80001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001754-27240.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001755-31153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001755-34093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001754-80001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001753-16371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001756-45424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001756-24474.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001756-40171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001756-32491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001757-16691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001743-75676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001743-75676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001744-95920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001744-51467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001744-85304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001744-90969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001745-86651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001745-64971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001745-82137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001745-76506.jpg)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001744-51467.png)
(2)求圆
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108001743-75676.png)
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