IGO 2022 I2

Two circles $\omega_1$ and $\omega_2$ with equal radius intersect at two points $E$ and $X$ . Arbitrary points $C, D$ lie on $\omega_1, \omega_2$ . Parallel lines to $XC, XD$ from $E$ intersect $\omega_2, \omega_1$ at $A, B$ , respectively. Suppose that $CD$ intersect $\omega_1, \omega_2$ again at $P, Q$ , respectively. Prove that $ABPQ$ is cyclic.

Proposed by Ali Zamani