The hanging chain problem with respect to a circle López Camino, Rafael Catenary Hanging problem Calculus of variations The author thanks Prof. Maciej Czarnecki for proposing the problem and acknowledges his hospitality at the University of Lodz during the preparation of this paper. This research is partially supported by MINECO/MICINN/FEDER grant no. PID2023-150727NB-I00, and by the “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105- M, funded by MCINN/AEI/10.13039/501100011033/ CEX2020-001105-M. Let S1 be a circle in the 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 S1. We describe the shape of such curves, distinguishing if the curves lie in the inside or outside of S1. We extend the problem for energies that are powers to the distance to S1. 2026-01-22T09:40:36Z 2026-01-22T09:40:36Z 2025 journal article López Camino, R. (2025). The hanging chain problem with respect to a circle. Kyungpook Mathematical Journal, vol. 65, no. 1, 131-147. https://doi.org/10.5666/KMJ.2025.65.1.131 1225-6951 0454-8124 https://hdl.handle.net/10481/110077 10.5666/KMJ.2025.65.1.131 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Kyungpook National University