2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74110Consider a continuous one parameter family of circles in complex plane that contains two circles lying in the exterior of one another. Under mild assumptions on the family, we prove that if a continuous function on the union of the above circles extends holomorphically into each circle, then the function is holomorphic in the interior of the union of the circles.Complex Variables30E25, 32V25text