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Quadrilateral and sum of angles

Source: Balkan Mathematical Olympiad 2007, problem 1.

April 28, 2007
trigonometrygeometrygeometric transformationreflectiontrapezoidcircumcircletrig identities

Problem Statement

Let ABCDABCD a convex quadrilateral with AB=BC=CDAB=BC=CD, with ACAC not equal to BDBD and EE be the intersection point of it's diagonals. Prove that AE=DEAE=DE if and only if ∠BAD+∠ADC=120\angle BAD+\angle ADC = 120.
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