One main result concerns a set \(E\) on the unit circle consisting of a fixed number \(n\) of arcs with total length \(L\). Let \(E^*\) be the set whose arcs have equal length \(L/n\) and are symmetrically distributed around the circle. Then \[ \hbox{cap} E\leq\hbox{cap} E^*=\{\sin L/4\}^{1/n}. \] The proof is obtained by clever use of results by Ahlfors, Dubinin, Fekete and the author herself. Other geometric configurations are also considered.