The MacBeath triangle
(a term coined here for the first time), is the triangle whose vertices are the contact
points of the MacBeath inconic with the reference
triangle .

It is the polar triangle of the MacBeath
inconic .

It has trilinear vertex matrix

(1)

It is perspective with the reference triangle , with perspector (corresponding to the
Brianchon point of the MacBeath
inconic ) given by Kimberling center , which has equivalent triangle center functions

It has area

(4)

where
is the area of the reference triangle .

The circumcircle of the MacBeath triangle is the
MacBeath circle .

See also MacBeath Inconic ,

MacBeath
Circle
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Cite this as:
Weisstein, Eric W. "MacBeath Triangle."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/MacBeathTriangle.html

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