角度EAF=ABE 因为相似三角形?

来源: 于 2014-11-26 13:33:25 [旧帖] [给我悄悄话] 本文已被阅读：次

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.