Four Coins Problem

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Given three coins of possibly different sizes which are arranged so that each is tangent to the other two, find the coin which is tangent to the other three coins. The solution is the inner Soddy Circle.

See also Apollonius Circles, Apollonius' Problem, Arbelos, Bend (Curvature), Circumcircle, Coin, Descartes Circle Theorem, Hart's Theorem, Pappus Chain, Soddy Circles, Sphere Packing, Steiner Chain

References

Oldknow, A. ``The Euler-Gergonne-Soddy Triangle of a Triangle.'' Amer. Math. Monthly 103, 319-329, 1996.