KöMaL 2025 B5458

Let $I$ be the incenter of triangle $ABC$, and let $AB<AC$. The perpendicular to $AI$ passing through $I$ intersects line $BC$ at $P$, and line segment $AP$ intersects the circumcircle of triangle $ABC$ at $Q$ for the second time. Prove that $IQ$ is perpendicular to $AP$.