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The analysis of the operational flexibility in power systems allows to identify the operational condition of an electrical network over all possible generating scenarios, its critical contingencies classified by their impact on the system, and other topics like limitations of the generation resources or requirements of load curtailment. A geometrical approach to determine and analyze power systems' secure regions is developed using Computational Geometry concepts, like Convex Hulls and Dirichlet Tessellations. This paper shows how the secure-operating region is calculated, following predefined reliability criteria, and how to quantify the operational flexibility through an index which takes into consideration the relative size of the aforementioned region. In addition, a novel contingency ranking based on the dominance of constraints is presented. This ranking is complemented by the notion of surrounding layers of the secure-operating region. The proposed formulation may be applied efficiently in large power systems.