Geodesic
Amicable Triangles and Perfect Circles
Journal for geometry and graphics, Tome 17 (2013) no. 1, pp. 53-67

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This is a contribution to triangle geometry. Two amicable triangles are inscribed in any circle which is related to a reference triangle ABC. Amicable triangles give rise to some family of circles – so-called perfect circles. In this way it is possible to generalize geometrical objects like the Soddy and Gergonne Line, the Gergonne Point, the Fletcher Point and the points of Eppstein, Griffith, Rigby and Nobbs as well. Amicable triangles and perfect circles have numerous and unusual interesting properties, and only a small part is presented in this article. Some of these results are still lacking of a rigorous mathematical proof; they only have been numerically confirmed.
Classification : 51M04
Mots-clés : Triangle geometry, amicable triangles, perfect circles, Soddy Line, Gergonne Point, Gergonne Line, Nobbs Points 
M. Sejfried. Amicable Triangles and Perfect Circles. Journal for geometry and graphics, Tome 17 (2013) no. 1, pp. 53-67. http://geodesic.mathdoc.fr/item/JGG_2013_17_1_JGG_2013_17_1_a4/
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