# On a Theorem in Geometry

Year of Award: 1968

Publication Information: The American Mathematical Monthly, vol. 74, 1967, pp. 627-640

Summary: The theorem under discussion is

"If four circles in a plane touch each other externally, and if $$r_1, r_2, r_3$$, and $$r_4$$ denote their curvatures (that is the reciprocals of their radii), then the following relation holds

$2(r_1^2 + r_2^2 + r_3^2 + r_4^2) = (r_1 + r_2 + r_3 + r_4)^2$

."

About the Author: (from The American Mathematical Monthly, vol. 74, (1967)) Daniel Pedoe was at the University of Minnesota at the time of publication.

MSC Codes:
97G40
Author(s):
Daniel Pedoe (University of Minnesota)
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Publication Date:
Wednesday, September 24, 2008
Publish Page:
Summary:

The theorem under discussion is,
"If four circles in a plane touch each other externally, and if $$r_1, r_2, r_3$$, and $$r_4$$ denote their curvatures (that is the reciprocals of their radii), then the following relation holds:

$2(r_1^2 + r_2^2 + r_3^2 + r_4^2) = (r_1 + r_2 + r_3 + r_4)^2$
."