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# Outer Soddy Circle

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

 (1)

where and are 8th-order and 16th-order polynomials, respectively.

The radius of the outer Soddy circle is

 (2) (3) (4) (5) (6) (7)

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

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

 (8) (9) (10)

where is the circumradius and is the -exradius of the reference triangle.

It has circle function

 (11)

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

No notable triangle centers lie on the outer Soddy circle.

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

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## References

Dergiades, N. "The Soddy Circles." Forum Geometricorum 7, 191-197, 2007. http://forumgeom.fau.edu/FG2007volume7/FG200726index.html.Kimberling, 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. https://mathworld.wolfram.com/OuterSoddyCircle.html