kissing circles problem

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist exactly two nonintersecting circles that are tangent to all three circles. These are called the inner and outer Soddy circles, and their centers are called the inner S and outer Soddy centers S', respectively. Frederick Soddy gave the formula for finding the radii of the Soddy circles (r_4) given the radii r_i (i = 1, 2, 3) of the other three.

Apollonian gasket | Apollonius circle | Apollonius' problem | arbelos | bend | bowl of integers | circumcircle | Descartes circle theorem | excentral triangle | four coins problem | Hart's theorem | inner Soddy center | inner Soddy circle | Malfatti circles | outer Soddy center | outer Soddy circle | Pappus chain | Soddy centers | Soddy triangles | sphere packing | Steiner chain | tangent circles | tangent spheres