Rad HAZU, Matematičke znanosti, Vol. 20 (2016), 83-95.

STEINER POINT OF A TRIANGLE IN AN ISOTROPIC PLANE

Ružica Kolar-Šuper, Zdenka Kolar-Begović and Vladimir Volenec

Department of Mathematics, University of Osijek, 31 000 Osijek, Croatia
e-mail: zkolar@mathos.hr

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: volenec@math.hr

Abstract.   The concept of the Steiner point of a triangle in an isotropic plane is defined in this paper. Some different concepts connected with the introduced concepts such as the harmonic polar line, Ceva’s triangle, the complementary point of the Steiner point of an allowable triangle are studied. Some other statements about the Steiner point and the connection with the concept of the complementary triangle, the anticomplementary triangle, the tangential triangle of an allowable triangle as well as the Brocard diameter and the Euler circle are also proved.

2010 Mathematics Subject Classification.   51N25.

Key words and phrases.   Isotropic plane, Steiner point, Steiner ellipse, Ceva’s triangle, orthic triangle.

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