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Journal for Geometry and Graphics 17 (2013), No. 1, 053--067
Copyright Heldermann Verlag 2013

Amicable Triangles and Perfect Circles

Michael Sejfried
ul. Zyzna 11F, 42200 Czestochowa, Poland

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.

Keywords: Triangle geometry, amicable triangles, perfect circles, Soddy Line, Gergonne Point, Gergonne Line, Nobbs Points.

MSC: 51M04

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