IMO 2007 Problem 2

Consider five points $A$ , $B$ , $C$ , $D$ and $E$ such that $ABCD$ is a parallelogram and $BCED$ is a cyclic quadrilateral. Let $\ell$ be a line passing through $A$ . Suppose that $\ell$ intersects the interior of the segment $DC$ at $F$ and intersects line $BC$ at $G$ . Suppose also that $EF = EG = EC$ . Prove that $\ell$ is the bisector of angle $DAB$ .

Author: Charles Leytem, Luxembourg