Question 32
Let $ABC$ be a triangle, $M$ be the midpoint of side $AC$ and $N$ be the midpoint of side $AB$. Let $r$ and $s$ be the reflections of lines $BM$ and $CN$ across line $BC$, respectively. Lines $r$ and $s$ meet line $MN$ at points $D$ and $E$, respectively. The circumcircles of $BDM$ and $CEN$ meet at points $X$ and $Y$, lines $BE$ and $CD$ meet at $Z$ and lines $r$ and $s$ meet at $W$. Prove that lines $XY$, $WZ$ and $BC$ meet at a single point.