RU-SPB 2010 Problem 103

$M,N$ are midpoints of $AB$ and $CD$ for convex quadrilateral $ABCD$ . Points $X$ and $Y$ are on $AD$ and $BC$ and $XD=3AX,YC=3BY$ . $\angle MXA=\angle MYB = 90$ . Prove that $\angle XMN=\angle ABC$