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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

 \[2(r_1^2 + r_2^2 + r_3^2 + r_4^2) = (r_1 + r_2 + r_3 + r_4)^2\]

 ."

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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:

\[2(r_1^2 + r_2^2 + r_3^2 + r_4^2) = (r_1 + r_2 + r_3 + r_4)^2\]
."

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