# On a Theorem in Geometry

by Daniel Pedoe (University of Minnesota)

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

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

."