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, illustrated above.
Four Coins Problem
See also
Apollonius Circle, Apollonius' Problem, Arbelos, Bend, Circumcircle, Coin, Descartes Circle Theorem, Hart's Theorem, Pappus Chain, Soddy Circles, Sphere Packing, Steiner Chain, Tangent CirclesExplore with Wolfram|Alpha
References
Oldknow, A. "The Euler-Gergonne-Soddy Triangle of a Triangle." Amer. Math. Monthly 103, 319-329, 1996.Referenced on Wolfram|Alpha
Four Coins ProblemCite this as:
Weisstein, Eric W. "Four Coins Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FourCoinsProblem.html