KöMaL 2020 B5135

The feet of the altitudes drawn from vertices $A$, $B$, $C$ of an acute-angled triangle $ABC$ are $A_1$, $B_1$ and $C_1$, respectively; and the midpoints of the altitudes $AA_1$ and $BB_1$ are $G$ and $H$, respectively. Prove that the circumscribed circle of triangle $C_1GH$ passes through the midpoint $F$ of side $AB$.