KöMaL 2008 B4069

The lengths of the tangents drawn from the points $A$ and $B$ to a circle $k$ are $a$ and $b$, respectively. $T$ is a point of the circle not collinear with $A$ and $B$ for which $\frac{AT}{a}=\frac{BT}{b}$ . Prove that the circle passing through the points $A$, $B$, $T$touches $k$.