In this paper, the Weber problem is considered. We demonstrate how the three existing points may be simultaneously tested for optimality by means of a simple geometrical construction.
Juel, H., & Love, R. F. (1986). A geometrical interpretation of the existing facility solution condition for the Weber problem. The Journal of the Operational Research Society, 37(12), 1129-1131. https://doi.org/10.2307/2582303