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China TST 2001 interior points of convex quadrilateral

Source: China TST 2001, problem 1

May 22, 2005
geometryChina

Problem Statement

EE and FF are interior points of convex quadrilateral ABCDABCD such that AE=BEAE = BE, CE=DECE = DE, ∠AEB=∠CED\angle AEB = \angle CED, AF=DFAF = DF, BF=CFBF = CF, ∠AFD=∠BFC\angle AFD = \angle BFC. Prove that ∠AFD+∠AEB=π\angle AFD + \angle AEB = \pi.
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