题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050408-64108.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-52620.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-10898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-93515.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-60859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-56083.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-74216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-86998.gif)
(1)当△AOB的面积达到最大值时,求四边形AOBM外接圆方程;
(2)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-49058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-79640.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-47713.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-62033.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-10898.gif)
当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-10898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-79170.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-35657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050411-21660.gif)
因
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-10898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050411-60106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050411-60106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050411-61747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050411-49325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050412-27713.gif)
此时△AOB的面积
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050412-92568.gif)
于是当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050412-85041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050412-27194.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-62033.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050413-98151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050413-14325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050413-90022.gif)
四边形AOBM外接圆方程方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-47713.gif)
(2)当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-10898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-79640.gif)
△AOB的面积等于4,符合题意; ………………………10分
当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050409-10898.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050413-10507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050412-27713.gif)
四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-79640.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050413-31320.gif)
于是有
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050414-39104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050414-14100.gif)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050413-14325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050414-90033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-62033.gif)
综上可知,△AOB的面积为8或
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050410-62033.gif)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050359-50088.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050359-67899.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050359-33018.gif)
(1)若AB=8,求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050359-33018.gif)
(2)当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050359-33018.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050359-16277.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050359-33018.gif)
(3)设AB的中点为N,试在平面上找一定点M,使MN的长为定值
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050353-92156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050353-86617.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050354-68628.gif)
求圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050353-92156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050344-62161.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050344-29631.gif)
相切于点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050345-74424.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050340-96504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050340-85629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050330-41584.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050331-72394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050331-88744.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023050331-33310.gif)
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