
Journal for Geometry and Graphics 09 (2005), No. 2, 155167 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. yiu@fau.edu 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, ninepoint circle, Feuerbach point. MSC: 51M04 [ Fulltextpdf (189 KB)] for subscribers only. 