IGO 2017 I2

Two circles $\omega_1,\omega_2$ intersect at $A,B$ . An arbitrary line through $B$ meets $\omega_1,\omega_2$ at $C,D$ respectively. The points $E,F$ are chosen on $\omega_1,\omega_2$ respectively so that $CE=CB,\ BD=DF$ . Suppose that $BF$ meets $\omega_1$ at $P$ , and $BE$ meets $\omega_2$ at $Q$ . Prove that $A,P,Q$ are collinear.

Proposed by Iman Maghsoudi