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Journal for Geometry and Graphics 09 (2005), No. 2, 155--167
Copyright Heldermann Verlag 2005

On Emelyanov's Circle Theorem

Paul Yiu
Dept. of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, U.S.A.

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.

Keywords: Emelyanov circle, homogeneous barycentric coordinates, infinite point, nine-point circle, Feuerbach point.

MSC: 51M04

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