Four Coins Problem


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.

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 Circles

Explore with Wolfram|Alpha


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

Referenced on Wolfram|Alpha

Four Coins Problem

Cite this as:

Weisstein, Eric W. "Four Coins Problem." From MathWorld--A Wolfram Web Resource.

Subject classifications