MathNet 2020 — Math Olympiad Vault — Part 01 Question 139

Three consecutive vertices $A$, $B$, and $C$ of a regular octagon (8-gon) are the centres of circles that pass through neighbouring vertices of the octagon. The intersection points $P$, $Q$, and $R$ of the three circles form a triangle (see figure).

Prove that triangle $PQR$ is equilateral.