题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030007-42934.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030007-48380.png)
解析
试题分析:在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030008-61646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030008-10626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030008-10626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030008-10626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030008-36386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030008-42279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030008-10626.png)
试题解析:设∠AOB=α, .1分
在△AOB中,由余弦定理得
AB2=OA2+OB2-2×OA×OBcos∠AOB
=12+22-2×1×2×cosα
=5-4cosα, .4分
于是,四边形OACB的面积为
S=S△AOB+S△ABC=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030009-38512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030009-65874.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030009-38512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030009-65874.png)
=sinα-
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030009-61299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030009-25681.png)
=2sin
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030009-36336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030009-25681.png)
因为0<α<π,所以当α-
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030010-19561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030010-41105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030007-48380.png)
即∠AOB=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030007-48380.png)
核心考点
试题【如图,半圆O的直径为2,A为直径延长线上的一点,OA=2,B为半圆上任意一点,以AB为一边作等边三角形ABC.问:点B在什么位置时,四边形OACB面积最大?】;主要考察你对解三角形应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030003-21397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030004-57930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030003-21397.png)
A.等腰三角形 | B.直角三角形 |
C.等腰或直角三角形 | D.等腰直角三角形 |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025957-34685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025957-63610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025957-86603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025957-28101.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025957-16946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025957-92167.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025957-48025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025957-87463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025947-79310.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025947-32399.png)
(2)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025947-45403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025947-27329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025942-67785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025942-79094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025942-86387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025942-32889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025942-21227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025942-62446.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020025936-65188.png)
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