Question 28
Let $\triangle ABC$ be an acute-angled triangle with $AC \lt AB$ and circumradius $R$. Furthermore, let $D$ be the foot of the 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: $\angle AST = 90^\circ$.
Prove: $\angle AST = 90^\circ$.