角度EAF=ABE 因为相似三角形?

来源: calligraphy 于 2014-11-26 13:33:25 [] [旧帖] [给我悄悄话] 阅读数 : 0 (517 bytes)
回答: 绕晕了，其实很简单。 由 soundofsilence 于 2014-11-26 11:25:56

角度标错了吧？

Let G be the mid-point of EC. Draw DG.

Rt. tris. DCE similar to ADE. Since G and F are mid-points of CE and DE, respectively. So Rt. tris. AFE similar to DGE, so angles FAE = GDE. subtract them from DAE=CDE, we have angles DAF=CDG.

Because DG // BE, so angles CDG=DBE, so angles DBE=DAF.

Let AF and BE intersect at M, we can conclude A, O, D and B are cyclic.

Finally angles AOB=ADB=90 degree. Q.E.D.

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• 多读了个条件，改一改。 -soundofsilence- ♀ 给 soundofsilence 发送悄悄话 soundofsilence 的博客首页 (177 bytes) () 11/26/2014 postreply 13:56:53

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