Coincidences of Centers of Plane Quadrilaterals

Abstract

We consider the three natural centers of mass associated with a general quadrilateral together with the Fermat–Torricelli center and explore the degree of regularity implied by the coincidence of two or more of these four centers. We then extend this investigation to include cyclic quadrilaterals, where we add the circumcenter to the list, and circumscriptible quadrilaterals, where we add the incenter.