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
 |
(1) |
(Coxeter and Greitzer 1967).
The inversive distance between the Soddy circles is given by
 |
(2) |
and the circumcircle and incircle of a triangle with circumradius 
and inradius 
are at inversive distance
 |
(3) |
(Coxeter and Greitzer 1967, pp. 130-131).
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References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 123-124 and 127-131, 1967.
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Cite this as:
Weisstein, Eric W. "Inversive Distance." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/InversiveDistance.html