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1 . 折纸是一项玩法多样的活动.通过折叠纸张,可以创造出各种各样的形状和模型,如动物、花卉、船只等.折纸不仅是一种艺术形式,还蕴含了丰富的数学知识.在纸片
中,A,B,C所对的边分别为a,b,c,
的面积为
,
.
(1)证明:
.
(2)若
,求
的值.
(3)在(2)的条件下,若
,D是AB的中点,现需要对纸片
做一次折叠,使C点与D点重合,求折叠后纸片重叠部分的面积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1225fd03e8e8730dac8487dae5387635.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e482cb92791ee3dc96e0a086e46cc23f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30dc055367efbff99618485781eeb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5201fc26d013f6fb889933c0e32f5c53.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
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