Question 107
Point $D$ is the intersection point of the angle bisector of vertex $A$ with side $BC$ of triangle $ABC$, and point $E$ is the tangency point of the inscribed circle of triangle $ABC$ with side $BC$. $A_1$ is a point on the circumcircle of triangle $ABC$ such that $AA_1 \parallel BC$. If we denote by $T$ the second intersection point of line $EA_1$ with the circumcircle of triangle $AED$ and by $I$ the incenter of triangle $ABC$, prove that $IT = IA$.