Belarus2022

Two circles ${\omega }_1$ and ${\omega }_2$ intersect each other at points $X$ and $Y$. Two lines pass through $Y$: one intersects ${\omega }_1$ and ${\omega }_2$ for the second time at points $A$ and $B$ respectively and another intersects ${\omega }_1$ and ${\omega }_2$ for the second time at points $C$ and $D$ respectively. The line $AD$ intersects ${\omega }_1$ and ${\omega }_2$ for the second time at points $P$ and $Q$ respectively such that $YP=YQ$. Prove that circumcircles of $△BCY$ and $△PQY$ touch each other. (Palina Chernikava)