Curves of centroids, Gergonne points and symmedian centers in triangle pencils in isotropic plane

In this paper we consider a triangle pencil in an isotropic plane consisting of the triangles that have the same circumscribed circle. We study the curves of centroids, Gergonne points and symmedian centers for such pencils of triangles. We also study the curves of centroids, Gergonne points and symmedian centers for tangential triangles of such a triangle pencil.