RS-SMO 2017 Problem 2

Let $ABCD$ be a convex and cyclic quadrilateral. Let $AD\cap BC=\{E\}$ , and let $M,N$ be points on $AD,BC$ such that $AM:MD=BN:NC$ . Circle around $\triangle EMN$ intersects circle around $ABCD$ at $X,Y$ prove that $AB,CD$ and $XY$ are either parallel or concurrent.