CONO-SUR 1998 Problem 2

Let $H$ be the orthocenter of the triangle $ABC$ , $M$ is the midpoint of the segment $BC$ . Let $X$ be the point of the intersection of the line $HM$ with arc $BC$ (without $A$ ) of the circumcircle of $ABC$ , let $Y$ be the point of intersection of the line $BH$ with the circle, show that $XY = BC$ .