KZ-MO 2001 Problem 2

In the acute triangle $ABC$ , $L$ , $H$ and $M$ are the intersection points of bisectors, altitudes and medians, respectively, and $O$ is the center of the circumscribed circle. Denote by $X$ , $Y$ and $Z$ the intersection points of $AL$ , $BL$ and $CL$ with a circle, respectively. Let $N$ be a point on the line $OL$ such that the lines $MN$ and $HL$ are parallel. Prove that $N$ is the intersection point of the medians of $XYZ$ .