Problem

Source: Latvian TST for Baltic Way 2020 P10

Tags: geometry, geometric transformation, reflection



Given $\triangle ABC$ and it's orthocenter $H$. Point $P$ is arbitrary chosen on the side $ BC$. Let $Q$ and $R$ be reflections of point $P$ over sides $AB, AC$. It is given that points $Q,H,R$ are collinear. Prove that $\triangle ABC$ is right angled.