Problem

Source: 2015 Saudi Arabia BMO TST I p3

Tags: geometry, circumcircle, incenter, tangent circles



Let $ABC$ be a triangle, $\Gamma$ its circumcircle, $I$ its incenter, and $\omega$ a tangent circle to the line $AI$ at $I$ and to the side $BC$. Prove that the circles $\Gamma$ and $\omega$ are tangent. Malik Talbi