BALKAN-SL 2012 G5

$\boxed{\text{G5}}$ The incircle of a triangle $ABC$ touches its sides $BC$ , $CA$ , $AB$ at the points $A_1$ , $B_1$ , $C_1$ .Let the projections of the orthocenter $H_1$ of the triangle $A_{1}B_{1}C_{1}$ to the lines $AA_1$ and $BC$ be $P$ and $Q$ ,respectively. Show that $PQ$ bisects the line segment $B_{1}C_{1}$