DE-BUNDESWETTBEWERB 2015 Problem 3

Let $M$ be the midpoint of segment $[AB]$ in triangle $\triangle ABC$ . Let $X$ and $Y$ be points such that $\angle{BAX}=\angle{ACM}$ and $\angle{BYA}=\angle{MCB}$ . Both points, $X$ and $Y$ , are on the same side as $C$ with respect to line $AB$ . Show that the rays $[AX$ and $[BY$ intersect on line $CM$ .