KöMaL 2008 A446

The lengths of tangents drawn from the points $A$, $B$ and $C$ to a sphere $s$ are $a$, $b$and $c$, respectively. $T$ is a point on the sphere, not co-planar with $A$, $B$ and $C$, such that $\frac{AT}{a}=\frac{BT}{b}=\frac{CT}{c}$ . Prove that the sphere passing through the points $A$, $B$, $C$, $T$ touches $s$.