Given three mutually tangent circles, there exist exactly two nonintersecting circles which are tangent circles to all three original circles. These are called the inner and outer Soddy circles, and their centers S and S' are called the inner and outer Soddy centers, respectively.

equal detour point | inner Soddy center | inner Soddy circle | isoperimetric point | outer Soddy center | outer Soddy circle | Soddy circles