engleski

On Harmonic Quadrangle in the Isotropic Plane

In this talk we present several results concerning the geometry of the harmonic quadrangle in the isotropic plane. We consider the standard cyclic quadrangle with the circumscribed circle given by y = x^2 and vertices are chosen to be A = (a, a^2), B = (b, b^2), C = (c, c^2), and D = (d, d^2), with a, b, c, d being mutually diff erent real numbers, where a < b < c < d. The harmonic quadrangle in the isotropic plane is the standard cyclic quadrangle with a special property: the vertices A, B, C and D are chosen in a way that tangents A and C at the vertices A and C, respectively, are intersected in the point incident with BD, and tangents B and D at the vertices B and D, respectively, are intersected in the point incident with AC. Accordingly, 2(ac + bd) = (a + c)(b + d) follows.

isotropic plane ; cyclic quadrangle ; harmonic quadrangle

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