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Inner Soddy Center


The inner Soddy center (or inner Soddy point) is the center of the inner Soddy circle. It is equivalent to the equal detour point X_(175) (Kimberling 1994) and has equivalent triangle center functions

alpha_(175)=1+sec(1/2A)cos(1/2B)cos(1/2C)
(1)
alpha_(175)=1+(bc)/(2(-a+b+c)R),
(2)

where R is the circumradius of the reference triangle.

It lies on the Soddy line.


See also

Inner Soddy Circle, Outer Soddy Center, Soddy Circles

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References

Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.

Referenced on Wolfram|Alpha

Inner Soddy Center

Cite this as:

Weisstein, Eric W. "Inner Soddy Center." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InnerSoddyCenter.html

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