KöMaL 2006 A410

The angle bisectors of triangle ABC intersect sides $BC$, $CA$ and $AB$ at points $A_1$, $B_1$ and $C_1$, respectively. On line $A_1 B_1$, denote by $F$ the perpendicular foot point of $C_1$. Prove that line $FC_1$ bisects angle AFB .