Let $ABC$ be a triangle and $I$ its incenter. The point $D$ is on segment $BC$ and the circle $\omega$ is tangent to the circumcirle of triangle $ABC$ but is also tangent to $DC, DA$ at $E, F$, respectively. Prove that $E, F$ and $I$ are collinear.
Problem
Source: 2016 Saudi Arabia BMO TST , level 4, III p2
Tags: geometry, incenter, tangent circles, collinear, circumcircle