Geodesic
On Emelyanov's Circle Theorem
Journal for geometry and graphics, Tome 9 (2005) no. 2, pp. 155-167.

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

Given a triangle and a point T, let Γ+(T) be the triad of circles each tangent to the circumcircle and to a side line at the trace of T. Assuming T an interior point and each circle tangent the circumcircle internally, Lev Emelyanov has shown that the circle tangent to each of these circles is also tangent to the incircle. In this paper, we study this configuration in further details and without the restriction to interior points. We identify the point of the tangency with the incircle, and derive some interesting loci related this configuration.
Classification : 51M04
Mots-clés : Emelyanov circle, homogeneous barycentric coordinates, infinite point, nine-point circle, Feuerbach point 
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     title = {On {Emelyanov's} {Circle} {Theorem}},
     journal = {Journal for geometry and graphics},
     pages = {155--167},
     publisher = {mathdoc},
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     number = {2},
     year = {2005},
     url = {http://geodesic.mathdoc.fr/item/JGG_2005_9_2_JGG_2005_9_2_a3/}
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P. Yiu . On Emelyanov's Circle Theorem. Journal for geometry and graphics, Tome 9 (2005) no. 2, pp. 155-167. http://geodesic.mathdoc.fr/item/JGG_2005_9_2_JGG_2005_9_2_a3/