Mandart inellipse

In geometry, the Mandart inellipse of a triangle is the inconic having parameters

$x:y:z=\frac{a}{b+c-a}:\frac{b}{a+c-b}:\frac{c}{a+b-c}$

where a, b, and c are sides of the triangle. It is named after H. Mandart, who studied it in two papers published in the late 19th century.^[1][2]

The center of the Mandart inellipse is the mittenpunkt of the triangle. The three lines connecting the triangle vertices to the opposite points of tangency all meet in a single point, the Nagel point of the triangle.^[1]

Notes

1. ^ ^{a b} Gibert, Bernard (2004), "Generalized Mandart conics", Forum Geometricorum 4: 177–198, http://forumgeom.fau.edu/FG2004volume4/FG200421.pdf .
2. ^ Mandart, H. (1893), "Sur l’hyperbole de Feuerbach", Mathesis: 81–89 ; Mandart, H. (1894), "Sur une ellipse associée au triangle", Mathesis: 241–245, http://books.google.com/books?id=kqAKAAAAYAAJ&pg=PA241 . As cited by Gibert (2004).

External links

• Weisstein, Eric W., "Mandart Inellipse" from MathWorld.

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