Smallest Circle Problem - Characterization

Characterization

Most of the geometric approaches for the problem look for points that lie on the boundary of the minimum circle and are based on the following simple facts:

• The minimum covering circle is unique.
• The minimum covering circle of a set S can be determined by at most three points in S which lie on the boundary of the circle. If it is determined by only two points, then the line segment joining those two points must be a diameter of the minimum circle. If it is determined by three points, then the triangle consisting of those three points is not obtuse.