Best Approximations of Convex Compact Sets by Balls in the Hausdorff Metric

We deduce an upper bound for the Hausdorff distance between a nonempty bounded set and the set of all closed balls in a strictly convex straight geodesic space X of nonnegative curvature. We prove that the set $\chi \left {\rm M} \right]$ of centers of closed balls approximating a convex compact set in the Hausdorff metric in the best possible way is nonempty _X M] and is contained in M. Some other properties of $\chi \left {\rm M} \right]$ also are investigated.