  In this article we use techniques developed by Hrushovski-Loeser to study
certain metric properties of the Berkovich analytification of a finite morphism
of smooth connected projective curves. In recent work, M. Temkin proved a
radiality statement for the topological ramification locus associated to such
finite morphisms. We generalize this result in two directions. We prove a
radiality statement for a more general class of sets which we call definable
sets. In another direction, we show that the result of Temkin can be obtained
in families.
