Geodesic
Cevian Cousins of a Triangle Centroid
Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 211-218 Cet article a éte moissonné depuis la source Heldermann Verlag

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According to Seebach's theorem there exist six points inside a triangle with Cevian triangles similar to the reference triangle. Besides the centroid, other five points M, M', MA, MB, MC are generally not constructable with ruler and compass. We present an access to these five points using an additional tool: a possibility to draw a conic through five given points. We provide information on barycentric coordinates of these five points and prove that MAMBMC is a central triangle of type 2 and that points M and M' are Brocardians of each other.
Classification : 51M15, 51N20, 51M04
Mots-clés : Cevian triangle, Seebach's theorem, constructability with ruler and compass, conics, central triangle, Brocardian 
@article{JGG_2015_19_2_JGG_2015_19_2_a4,
     author = {B. Hvala },
     title = {Cevian {Cousins} of a {Triangle} {Centroid}},
     journal = {Journal for geometry and graphics},
     pages = {211--218},
     year = {2015},
     volume = {19},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a4/}
}
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B. Hvala . Cevian Cousins of a Triangle Centroid. Journal for geometry and graphics, Tome 19 (2015) no. 2, pp. 211-218. http://geodesic.mathdoc.fr/item/JGG_2015_19_2_JGG_2015_19_2_a4/