IR-TST 2015 Problem 8

In triangle $ABC$ (with incenter $I$ ) let the line parallel to $BC$ from $A$ intersect circumcircle of $\triangle ABC$ at $A_1$ let $AI\cap BC=D$ and $E$ is tangency point of incircle with $BC$ let $EA_1\cap \odot (\triangle ADE)=T$ prove that $AI=TI$ .