Question 5
Circles $\omega_{1}$ and $\omega_{2}$ meet at $P$ and $Q$. Segments $AC$ and $BD$ are chords of $\omega_{1}$ and $\omega_{2}$ respectively, such that segment $AB$ and ray $CD$ meet at $P$. Ray $BD$ and segment $AC$ meet at $X$. Point $Y$ lies on $\omega_{1}$ such that $PY \parallel BD$. Point $Z$ lies on $\omega_{2}$ such that $PZ \parallel AC$. Prove that points $Q, X, Y, Z$ are collinear.