IGO 2019 A1

Circles $\omega_1$ and $\omega_2$ intersect each other at points $A$ and $B$ . Point $C$ lies on the tangent line from $A$ to $\omega_1$ such that $\angle ABC = 90^\circ$ . Arbitrary line $\ell$ passes through $C$ and cuts $\omega_2$ at points $P$ and $Q$ . Lines $AP$ and $AQ$ cut $\omega_1$ for the second time at points $X$ and $Z$ respectively. Let $Y$ be the foot of altitude from $A$ to $\ell$ . Prove that points $X, Y$ and $Z$ are collinear.

Proposed by Iman Maghsoudi