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Given four mutually tangent circles whose curvatures (curvature is the reciprocal of radius) are k1, k2, k3, and k4,
(k1+k2+k3+k4)2 = 2(k1+k2+k3+k4)
Note: one of the "circles" can be a straight line, which has zero curvature.
Mathworld: Descartes Circle Theorem
Wikipedia: Descartes'_theorem
Summary of geometrical theorems
Three Circles Puzzle can be solved using Descartes Circle Theorem
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