KöMaL 2005 B3809

The triangle ABC is isosceles, namely $AB$ = $BC$. The points $C_1$, $A_1$, $B_1$ lie on the sides $AB$, $BC$, $CA$, respectively, and such that $\angle BC_1 A_1$=$\angle CA_1 B_1$=$\angle$ CAB . The lines $BB_1$ and $CC_1$ meet at $P$. Prove that the quadrilateral $AB_1 PC_1$ is cyclic.