Problem

Source: USAJMO 2024/1

Tags: AMC, USA(J)MO, USAJMO, geometry, cyclic quadrilateral, AIME



Let $ABCD$ be a cyclic quadrilateral with $AB = 7$ and $CD = 8$. Point $P$ and $Q$ are selected on segment $AB$ such that $AP = BQ = 3$. Points $R$ and $S$ are selected on segment $CD$ such that $CR = DS = 2$. Prove that $PQRS$ is a cyclic quadrilateral. Proposed by Evan O'Dorney