名校
1 . 已知有两只蚂蚁小红和小白在单位圆上活动,且有点
,点
.
![](https://img.xkw.com/dksih/QBM/2022/5/1/2970051749396480/2970659656695808/STEM/7b69c0dd-dbf3-4f06-9154-09949c055dac.png?resizew=229)
(1)设小红所在位置为
,小白所在位置为
,
.不妨设
.那么小红和小白的直线距离为___________;
(2)如果小红和小白分别从
、
两点以相同的速度沿圆周分别以逆时针方向和顺时针方向爬行,且没有碰面.求两只蚂蚁所在位置(分别视为一个点)及
、
两点构成的四边形周长的最大值?
(3)如果小红和小白沿圆周随意溜达,这两只蚂蚁没有碰面且都没有在
点,那么这两只蚂蚁所在位置(分别视为一个点)和
点构成三角形.这类三角形周长最大值为___________;并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42f05b013e4b7166cbc87c5a83d6a85.png)
![](https://img.xkw.com/dksih/QBM/2022/5/1/2970051749396480/2970659656695808/STEM/7b69c0dd-dbf3-4f06-9154-09949c055dac.png?resizew=229)
(1)设小红所在位置为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05658511cc8728f4a77fbed890a637a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9faa86fd7ec41cacc3ff1859a9b1fc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c137e7ca5167b58df204c74db6c976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c61cfbfd3bf888856b7dc9b2a84c4a.png)
(2)如果小红和小白分别从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)如果小红和小白沿圆周随意溜达,这两只蚂蚁没有碰面且都没有在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
13-14高一·全国·课后作业
2 . 已知
为正数,用排序不等式证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88200e445dc471bb7a173536d0ebb70e.png)
您最近一年使用:0次
13-14高一·全国·课后作业
解题方法
3 . 设
为正数,利用排序不等式证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd228c27daed5420401b2119c332f3be.png)
您最近一年使用:0次