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 Skip Navigation LinksMath Help > Geometry > Circles, Conic Sections > Descartes Circle Theorem

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.

Internet references

Mathworld: Descartes Circle Theorem

Wikipedia: Descartes'_theorem

Related pages in this website:

Summary of geometrical theorems

Three Circles Puzzle can be solved using Descartes Circle Theorem

 

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