The hanging chain problem with respect to a circle

Let ${\text{s}}^1$ be a circle in Euclidean plane. We consider the problem of finding the shape of a planar curve which is an extremal of the potential energy that measures the distance to ${\text{s}}^1$. We describe the shape of these curves distinguishing if the curves lie in the inside or outside of ${\text{s}}^1$. We extend the problem for energies that are powers to the distance to ${\text{s}}^1$.