
Journal for Geometry and Graphics 10 (2006), No. 2, 125132 Copyright Heldermann Verlag 2006 On Feuerbach's Theorem and a Pencil of Circles in the Isotropic Plane J. BebanBrkic Dept. of Geomatics, Faculty of Geodesy, University of Zagreb, Kaciceva 26, 10000 Zagreb, Croatia jbeban@geof.hr R. KolarSuper Faculty of Teacher Education, University of Osijek, Lorenza Jägera 9, 31000 Osijek, Croatia rkolar@vusos.hr Z. KolarBegovic Dept. of Mathematics, University of Osijek, Gajev trg 6, 31000 Osijek, Croatia zkolar@mathos.hr V. Volenec Dept. of Mathematics, Univesity of Zagreb, Bijenicka c. 30, 10000 Zagreb, Croatia volenec@math.hr After adapting the wellknown Euler and Feuerbach theorems for the isotropic plane, the connection among the circumcircle, Euler circle, tangential circumcircle, and the polar circle of a given allowable triangle has been shown. It has been proved that all four circles belong to the same pencil of circles. There are two more interesting circles in this pencil. Keywords: Isotropic plane, triangle, Feuerbach theorem, pencil of circles. MSC: 51N25 [ Fulltextpdf (132 KB)] for subscribers only. 