Let $H$ be the orthocenter of a triangle $ABC$ and $L_1$, $L_2$ be two perpendicular lines through $H$. Let also $A_1$, $B_1$, $C_1$ be the intersections of $L_1$ with $BC$, $CA$, $AB$, and similarly $A_2$, $B_2$, $C_2$ the intersections of $L_2$ with $BC$, $CA$, $AB$. Then the midpoints of $A_1A_2$, $B_1B_2$, $C_1C_2$ are collinear