IGO 2019 I1

Two circles $\omega_1$ and $\omega_2$ with centers $O_1$ and $O_2$ respectively intersect each other at points $A$ and $B$ , and point $O_1$ lies on $\omega_2$ . Let $P$ be an arbitrary point lying on $\omega_1$ . Lines $BP, AP$ and $O_1O_2$ cut $\omega_2$ for the second time at points $X$ , $Y$ and $C$ , respectively. Prove that quadrilateral $XPYC$ is a parallelogram.

Proposed by Iman Maghsoudi