  We study a generalization of the weighted Fermat-Torricelli problem in the
plane, which is derived by replacing vertices of a convex polygon by 'small'
closed convex curves with weights being positive real numbers on the curves, we
also study its generalized inverse problem. Our solution of the problems is
based on the first variation formula of the length of line segments that
connect the weighted Fermat-Torricelli point with its projections onto given
closed convex curves. We find the 'plasticity' solutions for non-overlapping
circles with variable radius.
