Los Angeles Math Circle

1/17 -- High School II: Circumcenter of mass (Emmanuel Tsukerman)

We will define and study a variant of the center of mass of a polygon, called the circumcenter of mass. The circumcenter of mass is defined by triangulating the polygon, finding the circumcenter of each triangle, and taking the weighted average of those circumcenters, where each circumcenter is weighted by the area of its triangle. Analogues of the Archimedes Lemma and the Euler line result.