  A well-known object in classical Euclidean geometry is the circumcenter of a
triangle, i.e., the point that is equidistant from all vertices. The purpose of
this paper is to provide a systematic study of the circumcenter of sets
containing finitely many points in Hilbert space. This is motivated by recent
works of Behling, Bello Cruz, and Santos on accelerated versions of the
Douglas--Rachford method. We present basic results and properties of the
circumcenter. Several examples are provided to illustrate the tightness of
various assumptions.
