Let $M$ be the intersection of the medians $ABC$ of the triangle and the midpoint of the side $BC$. $A$ line parallel to side $BC$ and passing through point $M$ intersects sides $AB$ and $AC$ at points $X$ and $Y$ respectively. Let the point of intersection of the lines $XC$ and $MB$ be $Q$ and let $P$ intersection point of the lines $YB$ and $MC$ be $P$ . Prove that the triangles $DPQ$ and $ABC$ are similar.