There are many varieties of the Butterfly theorem in the Euclidean plane, [2], [5], [7], but also in the hyperbolic, [6], and the isotropic plane, [1]. In the paper [1] the Butterfly theorem is proved by using the analytical method on the affine model of the isotropic plane. In this paper, it is proved by using the synthetic method on the projective model. It was shown earlier that with any quadrangle inscribed into a circle, an infnite number of butterfly points is associated which are located on a conic, [5], [6]. Here we prove that the analogues of those theorems also hold in the isotropic plane.

Mathematics