A circle which is tangent to sides $AB$ and $BC$ of triangle $ABC$ is also tangent to its circumcircle at point $T$. If $I$ in the incenter of triangle $ABC$, show that $\angle ATI=\angle CTI$.
Problem
Source: MOP 2005 Homework - Blue Group #20
Tags: geometry, circumcircle, incenter, exterior angle, angle bisector, geometry unsolved