Question 50
Let $ABC$ be a triangle such that $|AB| = 6$ and $|BC| = 9$, and let the measure of the angle $\angle ABC$ be $120^\circ$. Let $P$ and $Q$ be points on the side $\overline{AC}$ such that the triangle $BPQ$ is equilateral. Determine the length of the segment $\overline{PQ}$.