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The minimum-spanning circle (MSC) of N points in the plane is the smalest circle that encloses these points. The problem of computing the MSC of N stochastically varying points in the plane is considered. We propose a solution to the problem that involves a heirarchy of learning automata. The automata used in this solution are the Absorbing discretized linear Inaction-Penalty (ADLIP) automata, which are the only known linear automata which are of an inaction-penalty type and yet asymptotically optimal.