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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