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

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

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.

See also Inner Soddy Circle ,

Outer Soddy Center ,

Soddy Circles ,

Tangent
Circles
Explore with Wolfram|Alpha
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

Subject classifications More... Less...