Question 8
Circles $\omega_{1}$ and $\omega_{2}$ intersect at points $A$ and $B$. Segment $PQ$ is tangent to $\omega_{1}$ at $P$ and to $\omega_{2}$ at $Q$, and $A$ is closer to $PQ$ than $B$. Point $X$ is on $\omega_{1}$ such that $PX \parallel QB$, and point $Y$ is on $\omega_{2}$ such that $QY \parallel PB$. Given that $\angle APQ = 30^{\circ}$ and $\angle PQA = 15^{\circ}$, find the ratio $AX / AY$.