Problem

Source: Balkan Mathematical Olympiad 2007, problem 1.

Tags: trigonometry, geometry, geometric transformation, reflection, trapezoid, circumcircle, trig identities



Let $ABCD$ a convex quadrilateral with $AB=BC=CD$, with $AC$ not equal to $BD$ and $E$ be the intersection point of it's diagonals. Prove that $AE=DE$ if and only if $\angle BAD+\angle ADC = 120$.