MathNet 2022-part-03 — 197 problems (EN–VI) Question 111

Let $ABC$ be a triangle with $AB = 2BC$. Points $P$ and $Q$ are chosen on the side $AB$ to satisfy $AP : PQ : QB = 1 : 2 : 3$. A point $R$ is chosen on the side $AC$ to satisfy $AR : RC = 1 : 2$. Show that $\angle PRQ = 90^\circ$.