Abstract: Two algorithms are here presented for solving the smallest circle coveing a point-set on a plane and the largest empty circle of a point-set on the plane. The point-set is first divided into a number of layers, then the largest circle not enclosing the points in S is solved for layer by layer and kept The circle of the largest radius is finally found out. For the smallest circle enclosing the point-set S, the algorithm solves for the convex hulls of the point-Set S, then for the smallest circle enclosing the vertex of the convex hulls is found.