Question 2
Circles $C_1$ and $C_2$ have radii $3$ and $7$ respectively. The circles intersect at distinct points $A$ and $B$. A point $P$ outside $C_2$ lies on the line determined by $A$ and $B$ at a distance of $5$ from the center of $C_1$. Point $Q$ is chosen on $C_2$ so that $PQ$ is tangent to $C_2$ at $Q$. Find the length of the segment $PQ$.