Inellipse tangent where the triangle's excircles touch its sides
Arbitrary triangle
Mandart inellipse (centered at mittenpunkt M)
Lines from triangle's excenters to each corresponding edge midpoint (concur at M)
Splitters (concur at Nagel point N)
In geometry, the Mandart inellipse of a triangle is an ellipse that is inscribed within the triangle, tangent to its sides at the contact points of its excircles (which are also the vertices of the extouch triangle and the endpoints of the splitters).[1] The Mandart inellipse is named after H. Mandart, who studied it in two papers published in the late 19th century.[2][3]
^Juhász, Imre (2012), "Control point based representation of inellipses of triangles" (PDF), Annales Mathematicae et Informaticae, 40: 37–46, MR 3005114.
^Gibert, Bernard (2004), "Generalized Mandart conics" (PDF), Forum Geometricorum, 4: 177–198.
^Mandart, H. (1893), "Sur l'hyperbole de Feuerbach", Mathesis: 81–89;
Mandart, H. (1894), "Sur une ellipse associée au triangle", Mathesis: 241–245. As cited by Gibert (2004).
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