Loci of centers in pencils of triangles in the isotropic plane

Abstract

In this paper we consider a triangle pencil in an isotropic plane consisting of those triangles that have two fixed vertices, while the third vertex is moving along a line. We study the curves of centroids, Gergonne points, symmedian points, Brocard points and Feuerbach points for such a pencil of triangles. 2020 Mathematics Subject Classification. 51N25.

Locus Curves in Triangle Families

“…In the same way, we can observe what will be the locus of a certain line, or other object associated to triangles in a triangle family. Some results in this area, especially for the Euclidean plane can be found in [1,2,4,9,10,12], while [5,6,7] deal with the situation in the isotropic plane. This paper contains a family of triangles whose basic elements are dual to the family of triangles in [4] but the resulting locus curves are different.…”