On Generalizations of Bundle Theorem and Miquel's Six Circles Theorem on the Plane

Abstract

Bundle theorem and Miquel’s six circles theorem are two well-known theorems that concern the property of a system of points on the plane, where some of quadruples of points are concyclic. In this paper we propose generalizations for these two theorems. We call a generalization of bundle theorem the first six conics theorem and a generalization of Miquel’s six circles theorem the second six conics theorem, as they are both related to six conics in their configuration. Based on these two generalizations, interesting results are also discussed.