SHARYGIN 2006 Problem 18

Two perpendicular lines are drawn through the orthocenter $H$ of triangle $ABC$ , one of which intersects $BC$ at point $X$ , and the other intersects $AC$ at point $Y$ . Lines $AZ, BZ$ are parallel, respectively with $HX$ and $HY$ . Prove that the points $X, Y, Z$ lie on the same line.