题目
题型:不详难度:来源:
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005202-28168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005203-47014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005203-58024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005203-47014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005203-56144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005203-47014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005203-79230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005204-79157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005204-35137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005204-73802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005204-24089.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005204-45609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005205-79213.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005205-63269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005205-88222.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005202-28168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005205-16264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-17415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-18105.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-52502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-95445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-30541.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005207-40182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005207-38684.png)
解析
试题分析:(Ⅰ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005202-28168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005205-16264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005207-53436.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-17415.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-18105.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005207-81812.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-95445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-30541.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005207-40182.png)
(Ⅱ) 由(Ⅰ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005206-17415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005208-60297.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005208-73794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005208-28761.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005208-66341.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005205-63269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005208-96476.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005209-86286.png)
由三角形内角和定理可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005209-64765.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005209-38796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005203-47014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005209-14455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005210-11780.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005210-86820.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005210-60599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005210-81011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005210-65977.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005211-85737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005211-54814.png)
点评:解题时要认真审题,仔细解答,注意弦切角定理的合理运用
核心考点
举一反三
如图,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-25764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-97535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-81847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-88706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-81847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-97535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-74715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-75277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-62735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-99825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005156-65031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005156-39878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005156-56703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005156-63737.jpg)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005155-88706.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005156-71497.png)
如图,AD是⊙O的直径,AB是⊙O的切线,M, N是圆上两点,直线MN交AD的延长线于点C,交⊙O的切线于B,BM=MN=NC=1,求AB的长和⊙O的半径.
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005147-34455.jpg)
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-41467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-98906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-16494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005138-23640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-48001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005139-77095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-44656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-64951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005140-89127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-46826.png)
(1)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-82576.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005141-65522.png)
如图,AB是⊙O的直径 ,AC是弦 ,∠BAC的平分线AD交⊙O于点D,DE⊥AC,交AC的延长线于点E.OE交AD于点F.
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005133-13797.png)
(1)求证:DE是⊙O的切线;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005133-52974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005133-37378.png)
如图,A,B,C,D四点在同一圆上,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005123-63950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005123-88373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005123-97463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005124-95318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005124-84430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005124-12323.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005124-30576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005125-92381.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005125-19638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108005125-60643.png)
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