AT-OEMO-REG 2016 Problem 4

Let $ABC$ be a triangle with $AC > AB$ and circumcenter $O$ . The tangents to the circumcircle at $A$ and $B$ intersect at $T$ . The perpendicular bisector of the side $BC$ intersects side $AC$ at $S$ .

(a) Prove that the points $A$ , $B$ , $O$ , $S$ , and $T$ lie on a common circle. (b) Prove that the line $ST$ is parallel to the side $BC$ .

(Karl Czakler)