2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63644We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in constant curvature surfaces. Our method is based on two new functionals--one for the Euclidean and one for the hyperbolic case. We show how Colin de Verdi`ere's, Br"agger's and Rivin's functionals can be derived from ours.33 pages, 12 figures, Appendix. Revised version. Appendix on cellular surfaces removed, references added and removed, typos corrected, a few minor changesGeometric TopologyComplex VariablesMetric Geometry52C26 (primary) 53A30 (secondary)text