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## On Some Properties of Non Cyclic Quadrangle in Isotropic Plane

Beban-Brkić, Jelena; Šimić, Marija, Volenec, Vladimir
On Some Properties of Non Cyclic Quadrangle in Isotropic Plane // Proceedings of 13th International Conference on Geometry and Graphics / Weiss, Gunter (ur.).
Dresden, 2008. str. 1-7 (predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)

Naslov
On Some Properties of Non Cyclic Quadrangle in Isotropic Plane

Autori
Beban-Brkić, Jelena ; Šimić, Marija, Volenec, Vladimir

Izvornik
Proceedings of 13th International Conference on Geometry and Graphics / Weiss, Gunter - Dresden, 2008, 1-7

Skup
13th Internationl Conference on Geometry and Graphics

Mjesto i datum
Dresden, Njemačka, 04-08.08.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Isotropic plane ; non cyclic quadrangle ; medial point ; focal line

Sažetak
Some properties of a non cyclic quadrangle in an isotropic plane are presented in this talk. Let A, B, C, D be any four points in an isotropic plane where any two of them are not parallel and any three are not incident with the same line. The figure consisting of these four points and their six joint lines is called a complete quadrangle and will be denoted by ABCD . A quadrangle is called standard if a special hyperbola with the equation xy=1 is circumscribed to it. In order to prove the properties of any non cyclic quadrangle, it is sufficient to prove the properties for the standard quadrangle. Firstly, the Euler circles of the triangles ABC, ABD, ACD, BCD of the quadrangle ABCD are studied together with the radical axes of their Euler circles and circumscribed circles. These orthics form the quadrilateral for which the median is obtained. Due to duality of the notions of the median and the focus of the non tangential quadrilateral, in the case of a non cyclic quadrangle the medial point and the focal line are introduced, and some of their properties are shown.

Izvorni jezik
Engleski

Znanstvena područja
Matematika