题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070150-78025.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070150-25028.gif)
解析
解:如图,连结BD,则有四边形ABCD的面积,
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070151-74066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070151-10553.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070151-95822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070151-65633.gif)
又由余弦定理,
在△ABD中,BD 2 = AB 2+AD 2-2AB · ADcosA =22+42-2×2×4cos A= 20-16cos A;
在△CDB中,BD 2 = CB 2+CD 2-2CB · CDcosC = 62+42-2×6×4cos C = 52-48cosC;
∴ 20-16cosA= 52-48cosC;
∵ cosC = -cosA,∴ 64cos A =-32,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070151-56659.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070150-25028.gif)
核心考点
举一反三
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070144-40651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070144-73245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070144-90895.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070145-17559.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070145-14360.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070139-53264.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070135-88048.gif)
A.30° | B.30°或150° | C.60° | D.60°或120° |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070131-47308.gif)
A.等腰三角形 | B.直角三角形 | C.等腰直角三角形 | D.等边三角形 |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020070128-22713.gif)
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