题目内容
(本题满分10分,第(1)小题4分,第(2)小题6分)如图,△ABC中,![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/70352.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/13/70353.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/14/70354.gif)
(1)求:
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/70355.gif)
(2)求:
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/70356.gif)
解:(1) 在
中,
∴
……(1分)
设
∴
∴
…(2分)
∴
………………………………………………………………(1分)
(2) ∵点
是
的中点,![](http://thumb.1010pic.com/pic1/imagenew2/czsx/6/70366.gif)
∴
…………………………………………………(1分)
∴
…………………………………………………(1分)
在
中,
∴
…(1分)
(解一)∴
…(1分)
(解二)∵![](http://thumb.1010pic.com/pic1/imagenew2/czsx/14/70374.gif)
在
中,
∴
∽
∴
…(2分)
∴
…(2分) ∴
∴
…(1分) 解析:
略
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/17/70357.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/70358.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/19/70359.gif)
设
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/0/70360.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/70361.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/70362.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/3/70363.gif)
(2) ∵点
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/4/70364.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/5/70365.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/6/70366.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/7/70367.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/9/70369.gif)
在
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/10/70370.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/70358.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/70372.gif)
(解一)∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/13/70373.gif)
(解二)∵
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/14/70374.gif)
在
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/70375.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/70376.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/17/70377.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/70378.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/19/70379.gif)
∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/0/70380.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/70381.gif)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/70382.gif)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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