Rad HAZU, Matematičke znanosti, Vol. 20 (2016), 97-107.

ON PARABOLAS RELATED TO THE CYCLIC QUADRANGLE IN ISOTROPIC PLANE

Marija Šimić Horvath, Vladimir Volenec and Jelena Beban-Brkić

Faculty of Architecture, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: marija.simic@arhitekt.hr

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

Faculty of Geodesy, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: jbeban@geof.hr


Abstract.   The geometry of the cyclic quadrangle in the isotropic plane has been discussed in [11]. Therein, its diagonal triangle and diagonal points were introduced. Hereby, we turn our attention to parabolas inscribed to non tangential quadrilaterals of the cyclic quadrangle. Non tangential quadrilaterals of the cyclic quadrangle are formed by taking its four sides out of six. Several properties of these parabolas related to diagonal points of the cyclic quadrangle are studied.

2010 Mathematics Subject Classification.   51N25.

Key words and phrases.   Isotropic plane, cyclic quadrangle, parabolas related to the cyclic quadrangle.


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