Cartesian formulas for curvature, circumradius, and circumcenter for any three two-dimensional points

This work presents a concise summary of the methodology used to fit a circle to any three 2D Cartesian points (non-collinear and distinct), determining its radius and center, and its relation to the curvature of a portion of a curve consisting of those three points.  Explicit equations solely dependent on the coordinates of the three points are provided for all of these quantities too.  Functions written in Python to calculate these values are also provided.