Question 61
Let $ABCD$ be a convex quadrilateral. Choose points $E$ and $F$ on the segment $AB$ and a point $G$ on the segment $CD$, such that the quadrilaterals $ABCG$, $AFCD$ and $EFGC$ are cyclic. Prove that $|AE| = |FB|$ if and only if the segments $AB$ and $CD$ are parallel.