A Complete Quadrilateral in Rectangular Coordinates

Abstract

A complete quadrilateral in the Euclidean plane is studied. The geometry of such quadrilateral is almost as rich as the geometry of a triangle, so there are lot of associated points, lines and conics. Hereby, the study was performed in the rectangular coordinates, symmetrically on all four sides of the quadrilateral with four parameters a, b, c, d. In this paper 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.

On Some Properties of a Complete Quadrangle

“…is incident to the point (13), the pedal of the normal to the line U from the point O. Because of the symmetry, it is incident to the pedals of the normal to the line V and W from the point O, respectively.…”

“…In our former work in [13], we analyzed a complete quadrilateral in a similar way. A complete quadrilateral is a set of four lines (sides of the quadrilateral), where none of two lines are parallel and none of the three are concurrent.…”