Often, straightforward notions from one mathematical domain, when altered even slightly, can become rich and rewarding investigations involving numerous additional domains -- particularly when the investigation includes rigorous proof. This study begins with a familiar high school geometry problem (namely finding the circumcentre of a triangle), extends it to the study of equidistance and analyses the problem using geometry in concert with a number of other mathematical areas to construct a new region called the Circumregion. Altogether, the beautiful and intricate interconnectedness of mathematics is both employed and demonstrated.