KöMaL 2016 B4812

Let $C_1$, $A_1$ and $B_1$ denote the feet of the altitudes drawn to sides $AB$, $BC$ and $CA$ of an acute-angled triangle $ABC$, respectively. The perpendicular projections of the orthocentre of triangle $ABC$ on the lines $A_1B_1$, $B_1C_1$, $C_1A_1$ are $C_2$, $A_2$ and $B_2$, respectively. Prove that the lines $AA_2$, $BB_2$ and $CC_2$ are concurrent, and their intersection lies on the Euler line of triangle $ABC$.