Geodesic
Equicevian Points and Cubics of a Triangle
Journal for geometry and graphics, Tome 18 (2014) no. 2, pp. 133-157 Cet article a éte moissonné depuis la source Heldermann Verlag

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A point P in the plane of a given triangle ABC is said to be equicevian if the cevians AAP, BBP, and CCP through P are of equal length. In this note, we see that the set Ω of equicevian points can be obtained via three cubic curves, and we give a complete description of Ω including also the imaginary solutions. There exist up to ten equicevian points, among them the four focal points of the Steiner circumellipse. Besides, we present properties of the so-called equicevian cubics which in the irreducible case are strophoids, i.e., rational and circular with orthogonal tangents at their node.
Classification : 51N20, 51M25, 51M15
Mots-clés : Equicevian points, equicevian cubics, strophoid, Steiner's circumellipse, focal points, focal curves, pedal curves, Marden's Theorem, Euclidean construction 
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     author = {S. Abu-Saymeh and M. Hajja and H. Stachel },
     title = {Equicevian {Points} and {Cubics} of a {Triangle}},
     journal = {Journal for geometry and graphics},
     pages = {133--157},
     year = {2014},
     volume = {18},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2014_18_2_JGG_2014_18_2_a0/}
}
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S. Abu-Saymeh; M. Hajja; H. Stachel . Equicevian Points and Cubics of a Triangle. Journal for geometry and graphics, Tome 18 (2014) no. 2, pp. 133-157. http://geodesic.mathdoc.fr/item/JGG_2014_18_2_JGG_2014_18_2_a0/