数学课上,李老师出示了如下框中的题目.
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image001.png)
小敏与同桌小聪讨论后,进行了如下解答:
(1)特殊情况,探索结论
当点
为
的中点时,如图1,确定线段
与
的大小关系,请你直接写出结论:
(填“>”,“<”或“=”).
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image006.png)
(2)特例启发,解答题目
解:题目中,
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image004.png)
与
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image005.png)
的大小关系是:
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image005.png)
(填“>”,“<”或“=”).
理由如下:如图2,过点
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image002.png)
作
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image007.png)
,交
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image008.png)
于点
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image009.png)
. (请你接着完成以下解答过程)
(3)拓展结论,设计新题
在等边三角形
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image0010.png)
中,点
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image002.png)
在直线
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image003.png)
上,点
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image0011.png)
在直线
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image0012.png)
上,且
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image0013.png)
.若
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image0014.png)
的边长为3,AE=1,则
![](https://media.youtike.com//ques/201503/10/46e42625-5e25-4655-8fa7-85eeae22171a/image0015.png)
的长为
(请你直接写出结果).