The Mandart inellipse of a triangle is the inconic
with inconic parameters
Its center is the mittenpunkt 
of the triangle
and its Brianchon point is the Nagel
point 
.
The Mandart ellipse touches the sides of the triangle in the vertices of the extouch
triangle, which is also its polar triangle.
It has area
where 
is the area of the reference
triangle.
The only point out of the first 2676 Kimberling centers through which it passes is the Feuerbach
point 
(Weisstein, Oct. 16, 2004).
The Mandart inellipse is confocal with the billiard circumellipse (Reznik and Garcia
2021, p. 49).
See also
Brianchon Point,
Extouch
Triangle,
Inconic
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References
Gibert, B. "Generalized Mandart Conics." Forum Geom. 4, 177-198, 2004. https://web.archive.org/web/20230328092007/https://forumgeom.fau.edu/FG2004volume4/FG200421index.html.Mandart,
H. "Sur l'hyperbole de Feuerbach." Mathesis 13, 81-89, 1893.Mandart,
H. "Sur une ellipse associée au triangle." Mathesis 14,
241-245, 1894.Reznik, D. and Garcia, R. "Circuminvariants of 3-Periodics
in the Elliptic Billiard." Int. J. Geom. 10, 31-57, 2021. https://ijgeometry.com/wp-content/uploads/2020/12/3.-31-57.pdf.Referenced
on Wolfram|Alpha
Mandart Inellipse
Cite this as:
Weisstein, Eric W. "Mandart Inellipse."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MandartInellipse.html
Subject classifications
![A=pi((a+b-c)(b+c-a)(c+a-b))/([2(ab+bc+ca)-(a^2+b^2+c^2)]^(3/2))Delta,](/images/equations/MandartInellipse/NumberedEquation2.svg)
