AT-OEMO-REG 2020 Problem 3

Let a triangle $ABC$ be given with $AB <AC$ . Let the inscribed center of the triangle be $I$ . The perpendicular bisector of side $BC$ intersects the angle bisector of $BAC$ at point $S$ and the angle bisector of $CBA$ at point $T$ . Prove that the points $C, I, S$ and $T$ lie on a circle.

(Karl Czakler)