RU-SPB 2020 Problem 95

Point $I_a$ is the $A$ -excircle center of $\triangle ABC$ which is tangent to $BC$ at $X$ . Let $A'$ be diametrically opposite point of $A$ with respect to the circumcircle of $\triangle ABC$ . On the segments $I_aX, BA'$ and $CA'$ are chosen respectively points $Y,Z$ and $T$ such that $I_aY=BZ=CT=r$ where $r$ is the inradius of $\triangle ABC$ . Prove that the points $X,Y,Z$ and $T$ are concyclic.