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Show that the angles are equal

Source: Iran Third Round MO 1998, Exam 1, P2

July 23, 2009
geometrycyclic quadrilateralgeometry unsolved

Problem Statement

Let ABCDABCD be a convex pentagon such that ∠DCB=∠DEA=90∘, and DC=DE.\angle DCB = \angle DEA = 90^\circ, \ \text{and} \ DC=DE. Let FF be a point on AB such that AF:BF=AE:BCAF:BF=AE:BC. Show that ∠FEC=∠BDC, and ∠FCE=∠ADE.\angle FEC= \angle BDC, \ \text{and} \ \angle FCE= \angle ADE.
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