| Abstrakt: |
In this paper we study a complete quadrangle in the Euclidean plane that has a rectangular hyperbola circumscribed to it. Hereby, the approach is based on the rectangular coordinates and we prove the following main result: Let ABCD be a complete quadrangle and l a , l b , l c , l d mutually parallel lines through the circumcenters of BCD, ACD, ABD, ABC, respectively. Orthopoles of the lines l a , l b , l c , l d with respect to the triangles BCD, ACD, ABD, ABC lie on a line which passes through the center of the rectangular hyperbola H circumscribed to ABCD, and it is antiparallel to the given lines with respect to the axes of the hyperbola H . [ABSTRACT FROM AUTHOR] |
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