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MacBeath Circumconic


MacBeathCircumconic

The MacBeath circumconic is the dual conic to the MacBeath inconic, introduced in Dec. 2004 by P. Moses (Kimberling). It has circumconic parameters

 x:y:z=cosA:cosB:cosC,
(1)

and so has trilinear equation

 (cosA)/alpha+(cosB)/beta+(cosC)/gamma=0.
(2)

Its center is the symmedian point K.

When it is a circumellipse, it has area

 A=(2pisqrt(2)abcsqrt(secAsecBsecC))/((a^2+b^2+c^2)^(3/2))Delta.
(3)

The conic passed through Kimberling centers X_i for i=110 (the focus of the Kiepert parabola), 287, 648 (the trilinear pole of the Euler line), 651, 677, 895, 1331, 1332, 1797, 1813, 1814, and 1815.


See also

Circumconic, MacBeath Inconic

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References

Kimberling, C. "Encyclopedia of Triangle Centers: X(2967)=1st MacBeath Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X2967.

Referenced on Wolfram|Alpha

MacBeath Circumconic

Cite this as:

Weisstein, Eric W. "MacBeath Circumconic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MacBeathCircumconic.html

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