Journal for Geometry and Graphics 10 (2006), No. 2, 125--132
Copyright Heldermann Verlag 2006
On Feuerbach's Theorem and a Pencil of Circles in the Isotropic Plane
J. Beban-Brkic
Dept. of Geomatics, Faculty of Geodesy, University of Zagreb, Kaciceva 26, 10000 Zagreb, Croatia
jbeban@geof.hr
R. Kolar-Super
Faculty of Teacher Education, University of Osijek, Lorenza Jägera 9, 31000 Osijek, Croatia
rkolar@vusos.hr
Z. Kolar-Begovic
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 well-known 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
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