Problem

Source: Iranian TST 2019, third exam day 2, problem 4

Tags: geometry, geometric transformation, reflection, circumcircle



Given an acute-angled triangle $ABC$ with orthocenter $H$. Reflection of nine-point circle about $AH$ intersects circumcircle at points $X$ and $Y$. Prove that $AH$ is the external bisector of $\angle XHY$. Proposed by Mohammad Javad Shabani