Isoptic Point of the Non-Cyclic Quadrangle in the Isotropic Plane

We study the non-cyclic quadrangle ABCD in the isotropic plane and its isoptic point. This is a continuation of the research carried out in a few previous papers. There, we put the non-cyclic quadrangle in the standard position, which enables us to prove its properties using a simple analytical method. In the standard position, the special hyperbola xy=1 is circumscribed to the quadrangle. Hereby, we use the same method to obtain several results related to the isoptic point of the non-cyclic quadrangle. The isoptic point T is the inverse image of points A′, B′, C′, D′ with respect to circumcircles of BCD, ACD, ABD, ACD, respectively, where A′, B′, C′, D′ are isogonal points to vertices A, B, C, D with respect to triangles BCD, ACD, ABD, ACD. The circumircles are seen from T under the equal angles. Our analysis is motivated by the Euclidean results already published in the literature.