MK-MO 2015 Problem 1

Let $AH_A, BH_B$ and $CH_C$ be altitudes in $\triangle ABC$ . Let $p_A,p_B,p_C$ be the perpendicular lines from vertices $A,B,C$ to $H_BH_C, H_CH_A, H_AH_B$ respectively. Prove that $p_A,p_B,p_C$ are concurrent lines.