engleski

Power of the Point and the Line with respect to the Circle in the Isotropic Plane

The power of the point and the line with respect to the circle in the isotropic plane are studied in this presentation. The obtained results are applied in the investigation of properties of the non cyclic quadrangle in the isotropic plane. Hence, the radical axis and the radical center of circles in the isotropic plane are presented. As the principle of duality is preserved in the isotropic plane, notions dual to the radical axis and to the radical center, the umbilic point and the umbilic axis respectively, are introduced. Non cyclic quadrangle is called standard if a special hyperbola with the equation xy = 1 is circumscribed to it. The properties of the standard quadrangle related to the umbilic point and the umbilic axis of the circles are given.

isotropic plane; radical center; radical axis; umbilic point; umbilic axis

nije evidentirano