Speaker
Description
We study the properties of a complete quadrangle in the Euclidean plane. Many of them are known from earlier, published in different journals and periods and proved each using different methods. Hereby, we use rectangular coordinates symmetrically on four vertices and four parameters $a, b, c, d$ and prove all properties by the same analytical method. We put the complete quadrangle into such a coordinate system that its circumscribed hyperbola is rectangular. This is possible for each quadrangle for which the opposite sides are not perpendicular. We are focused on the properties of a complete quadrangle related to the center and anticenter of the quadrangle where the center of the quadrangle is the center of its circumscribed rectangular hyperbola and the anticenter of the quadrangle is the point symmetric to the center with respect to the centroid of the quadrangle. In this procedure, we obtain some new results as well.
