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Mandart Inellipse

MandartInellipse

The inconic having inconic parameters

x:y:z=a/(b+c-a):b/(a+c-b):c/(a+b-c).

Its center is the mittenpunkt M of the triangle and its Brianchon point is the Nagel point Na.

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

A=pi((a+b-c)(b+c-a)(c+a-b))/([2(ab+bc+ca)-(a^2+b^2+c^2)]^(3/2))Delta,

where Delta 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 X_(11) (Weisstein, Oct. 16, 2004).

See also

Brianchon Point, Extouch Triangle, Inconic

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References

Gibert, B. "Generalized Mandart Conics." Forum Geom. 4, 177-198, 2004. http://forumgeom.fau.edu/FG2004volume4/FG200421index.html.Mandart H. "Sur l'hyperbole de Feuerbach." Mathesis, 81-89, 1893.Mandart, H. "Sur une ellipse associée au triangle." Mathesis, 241-245, 1894.

Referenced on Wolfram|Alpha

Mandart Inellipse

Cite this as:

Weisstein, Eric W. "Mandart Inellipse." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MandartInellipse.html

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