Circles $\omega_1$ and $\omega_2$ intersect at $X$ and $Y$. Through point $Y$ two lines pass, one of which intersects $\omega_1$ and $\omega_2$ for the second time at $A$ and $B$, and the other at $C$ and $D$. Line $AD$ intersects for the second time circles $\omega_1$ and $\omega_2$ at $P$ and $Q$. It turned out that $YP=YQ$ Prove that the circumcircles of triangles $BCY$ and $PQY$ are tangent to each other.