Let $ABC$ be an acute triangle with incircle $\omega$, incenter $I$, and $A$-excircle $\omega_{a}$. Let $\omega$ and $\omega_{a}$ meet $BC$ at $X$ and $Y$, respectively. Let $Z$ be the intersection point of $AY$ and $\omega$ which is closer to $A$. The point $H$ is the foot of the altitude from $A$. Show that $HZ$, $IY$ and $AX$ are concurrent. Proposed by Nikola Velov
Problem
Source: 3rd Memorial Mathematical Competition "Aleksandar Blazhevski - Cane"- Junior D2 P5/ Senior D2 P4
Tags: geometry, concurrence, excircle, incircle, altitude