
Journal for Geometry and Graphics 18 (2014), No. 1, 061071 Copyright Heldermann Verlag 2014 A Triad of Circles Externally Tangent to the NinePoint Circle and Internally Tangent to Two Sides of a Triangle Boris Odehnal Abteilung für Geometrie, Universität für Angewandte Kunst, OskarKokoschkaPlatz 2, 1010 Wien, Austria boris@geometrie.tuwien.ac.at We determine the three circles in the interior of an acute triangle Δ which touch the ninepoint circle n from the outside and two sides of Δ from the inside. Some perspective triangles related to Δ and the three circles are found. A more general result on tangent triangles related to Apollonian configurations of circles leads to a specific result in the case of a special Apollonian configuration derived from the three circles in question. All constructions are linear once the excircles of the base triangle are constructed. Keywords: Triangle, ninepoint circle, Apollonian problem, tangent triangle, perspective triangles. MSC: 51N20 [ Fulltextpdf (157 KB)] for subscribers only. 