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Steiner Circle

SteinerCircle

The Steiner circle is the central circle with center at the nine-point center X_5 and radius

R_S=3/2R,

where R is the circumradius of the reference triangle.

It is the circumcircle of the Steiner deltoid.

It has circle function

l=-(-a^6+3a^4b^2-3a^2b^4+b^6+3a^4c^2+6a^2b^2c^2-b^4c^2-3a^2c^4-b^2c^4+c^6)/(4bc(-a+b-c)(a+b-c)(-a+b+c)(a+b+c)),

which is not a Kimberling center.

The Steiner circle does not pass through any Kimberling centers.

See also

Central Circle, Second Steiner Circle, Steiner Deltoid

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References

Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, 1967.

Referenced on Wolfram|Alpha

Steiner Circle

Cite this as:

Weisstein, Eric W. "Steiner Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SteinerCircle.html

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