IT-CESENATICO 2001 Problem 5

Let $ABC$ be a triangle and $\gamma$ the circle inscribed in $ABC$ . The circle $\gamma$ is tangent to side $AB$ at the point $T$ . Let $D$ be the point of $\gamma$ diametrically opposite to $T$ , and $S$ the intersection point of the line through $C$ and $D$ with side $AB$ . Prove that $AT=SB$ .