KöMaL 2009 A470

In the triangle ABC , denote by $A_1$, $B_1$, and $C_1$ the feet of altitudes. Let $P$ be the perpendicular foot $C_1$ on line $A_1 B_1$, and let $Q$ be that point of line $A_1 B_1$ for which $AQ$=$BQ$. Show that $\angle$ PAQ =$\angle$ PBQ =$\angle PC_1 C$.