engleski

Diagonal Triangle of a Non Tangential Quadrilateral in an Isotropic Plane

Properties of the non tangential quadrilateral ABCD in the isotropic plane are studied in this talk. A quadrilateral is called standard if a parabola with the equation x = y^2 is inscribed in it. Every non tangential quadrilateral can be represented in the standard position. In order to prove the properties of any non tangential quadrilateral, it is sufficient to prove the properties for the standard quadrilateral. The notions of the focus and the median of the quadrilateral are introduced and coordinates of the vertices and the equations of the sides of its diagonal triangle are given. It is shown that the midlines of the diagonal triangle touch the inscribed parabola of the quadrilateral. Furthermore, quadrilaterals formed by two diagonals and some two sides of the non tangential quadrilateral ABCD are studied and a few theorems on its foci are presented.

isotropic plane ; non tangential quadrilateral ; focus ; median ; diagonal triangle

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