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Given three mutually tangent Circles, there exist exactly two nonintersecting Circles
Tangent to all three Circles. These are called the inner and outer Soddy Circles, and
their centers are called the inner and outer Soddy points. The outer Soddy circle is the solution to the Four
Coins Problem. The center 
of the inner Soddy circle is the Equal Detour Point, and the center of the outer
Soddy circle 
is the Isoperimetric Point (Kimberling 1994).
See also Equal Detour Point, Isoperimetric Point, Soddy Circles
References
Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, p. 181, 1994.