The lengths of the tangents drawn from the points $\displaystyle A$ and $\displaystyle B$ to a circle $\displaystyle k$ are $\displaystyle a$ and $\displaystyle b$, respectively. We know that $\displaystyle \frac{AT}{a}=\frac{BT}{b}$ (and $\displaystyle A, B, T$ are not collinear.) Prove that the circle passing through the points $\displaystyle A, B, T$ touches $\displaystyle k$.