AT-OEMO-FED1 2015 Problem 2

Let $ABC$ be an acute-angled triangle with $AC < AB$ and circumradius $R$ . Furthermore, let $D$ be the foot ofthe altitude from $A$ on $BC$ and let $T$ denote the point on the line $AD$ such that $AT = 2R$ holds with $D$ lying between $A$ and $T$ . Finally, let $S$ denote the mid-point of the arc $BC$ on the circumcircle that does not include $A$ .

Prove: $\angle AST = 90^\circ$ .

(Karl Czakler)