engleski

On Complete Quadrilateral in Rectangular Coordinates

A complete quadrilateral in the Euclidean plane is studied. The geometry of such quadrilateral is almost as rich as the geometry of triangle, so there are lot of associated points, lines and conics. Hereby, the study was performed in the rectangular coordinates, symmetricaly on all four sides of the quadrilateral with four parameters a, b, c, d. In this part we will study the properties of some points, lines and circles associated to the quadrilateral. All these properties are well known, but here they are all proved by the same method. During this process, still some new results have appeared. For example: Parabolas circumscribed to trilaterals formed by three sides of the quadrilateral with axes parallel to the axis of parabola P inscribed to that quadrilateral arises from each other by using translations. They have parameter equal to the quarter of the parameter of P.

Euclidean plane ; complete quadrilateral ; parabola

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