MathNet 2017-part-07 — 172 problems (EN–VI) Question 130

Triangle $ABC$ has side lengths $AB = 15$, $BC = 18$, $CA = 20$. Extend $CA$ and $CB$ to points $D$ and $E$ respectively such that $DA = AB = BE$. Line $AB$ intersects the circumcircle of $CDE$ at $P$ and $Q$. Find the length of $PQ$.