Given three positive real numbers $r_1,r_2,r_3\in\mathbb{R}$, what is the necessary and sufficient condition that when I take 3 circles each tangent to each other of radii $r_1,r_2,r_3$ respectively, there is a circle bounding all of them and tangent to all of them?
For example, if $r_1=r_2=r_3$ then I can always find such a circle, however if $r_1=r_2$ and $r_1>r_3$ then it seems like it is not possible to find such a circle.
