In previous papers, the authors of this paper formulated a single facility minisum location problem, where the set of customers as well as the new facility may be represented as areas on the plane and the rectangular norm was used as the distance function [see Naval Res. Logist. 47, 77--84 (2000; Zbl 0953.90033
) and Comput. Oper. Res. 29, 625--636 (2002; Zbl 1001.90042
)]. Now they examine the case of the Euclidean norm. A number of properties of the problem are derived and algorithms for solving it are suggested.