Outer Soddy Circle


The outer Soddy circle is the solution to the four coins problem. It has circle function


where f(a,b,c) and g(a,b,c) are 8th-order and 16th-order polynomials, respectively.

The radius of the outer Soddy circle is


where Delta is the area of the reference triangle, R is the circumradius, r is its inradius, s is the semiperimeter, and S=2Delta is Conway triangle notation (P. Moses, pers. comm., Feb. 25, 2005; Dergiades 2007).

Its center, known as outer Soddy center, is the isoperimetric point X_(175) (Kimberling 1994), which has identical triangle center functions


where R is the circumradius and r_A is the A-exradius of the reference triangle.

It has circle function


(P. Moses, pers. comm., Feb. 25, 2005), where r_A, r_B, and r_C are the exradii.

No notable triangle centers lie on the outer Soddy circle.

See also

Inner Soddy Circle, Outer Soddy Center, Soddy Circles, Tangent Circles

Explore with Wolfram|Alpha


Dergiades, N. "The Soddy Circles." Forum Geometricorum 7, 191-197, 2007., C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.

Referenced on Wolfram|Alpha

Outer Soddy Circle

Cite this as:

Weisstein, Eric W. "Outer Soddy Circle." From MathWorld--A Wolfram Web Resource.

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