A geometry problem by Ilham Saiful Fauzi

Circles $C_{1}$ and $C_{2}$ have the same center.
Radius of $C_{1}$ is $4$ and radius of $C_{2}$ is 6.

A chord $AB$ of $C_{1}$ with length $1$ is extended until it intersects $C_{2}$ at points $P$ and $Q$ .
Find the length of chord $PQ$ .