BG-MO 2006 Problem 5

The triangle $ABC$ is such that $\angle BAC=30^{\circ},\angle ABC=45^{\circ}$ . Prove that if $X$ lies on the ray $AC$ , $Y$ lies on the ray $BC$ and $OX=BY$ , where $O$ is the circumcentre of triangle $ABC$ , then $S_{XY}$ passes through a fixed point.

Emil Kolev