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We study a generalization of the weighted Fermat-Torricelli problem in theplane, which is derived by replacing vertices of a convex polygon by 'small'closed convex curves with weights being positive real numbers on the curves, wealso study its generalized inverse problem. Our solution of the problems isbased on the first variation formula of the length of line segments thatconnect the weighted Fermat-Torricelli point with its projections onto givenclosed convex curves. We find the 'plasticity' solutions for non-overlappingcircles with variable radius.

The plasticity of non-overlapping convex sets in R^{2}