KöMaL 2019 C1537

A circle $k_1$ of radius $6$ and a circle $k_2$ of radius $3$ touch each other on the outside, and each of them touches a circle $k$ of radius 9 on the inside. One common exterior tangent of $k_1$ and $k_2$ intersects circle $k$ at points $P$ and $Q$. Determine the length of the line segment $PQ$.