In an obtuse triangle $ABC$, for which $AC < AB$, the radius of the inscribed circle is $R$, the midpoint of its arc $BC$ (which does not contain $A$) is $S$. A point $T$ is placed on the extension of altitude $AD$ such that $D$ is between $ A$ and $T$ and $AT = 2R$. Prove that $\angle AST = 90^o$.