Geodesic
The Gergonne Conic
Journal for geometry and graphics, Tome 15 (2011) no. 1, pp. 19-28.

Voir la notice de l'article provenant de la source Heldermann Verlag

The notion of Gergonne point was generalized in several ways during the last decades. Given a triangle V1V2V3, a point I and three arbitrary directions qi, we find a distance x = IQ1 = IQ2 = IQ3 along these directions, for which the three cevians ViQi are concurrent. If I is the incenter, qi are the direction of the altitudes, and x is the radius of the incenter, the point of concurrency is the Gergonne point. For arbitrary directions qi, it is shown that each point I generally yields two solutions, and points of concurrency lie on a conic, which can be called the Gergonne conic.
Classification : 51M04, 51N35
Mots-clés : Gergonne point, conics, projectivity, pencil of conics 
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S. Gorjanc; M. Hoffmann . The Gergonne Conic. Journal for geometry and graphics, Tome 15 (2011) no. 1, pp. 19-28. http://geodesic.mathdoc.fr/item/JGG_2011_15_1_JGG_2011_15_1_a1/