## Inversive Distance

The inversive distance is the Natural Logarithm of the ratio of two concentric circles into which the given circles can be inverted. Let be the distance between the centers of two nonintersecting Circles of Radii and . Then the inversive distance is

(Coxeter and Greitzer 1967).

The inversive distance between the Soddy Circles is given by

and the Circumcircle and Incircle of a Triangle with Circumradius and Inradius are at inversive distance

(Coxeter and Greitzer 1967, pp. 130-131).

References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 123-124 and 127-131, 1967.