Geometric Construction of the Fermat Point (120° Criterion) and Distance-Sum Min

This example demonstrates how to construct the Fermat point of a triangle and verify its defining property: each side is “seen” under a 120° angle from the Fermat point. It also illustrates the optimization interpretation that this point minimizes the sum of distances to the three vertices. The key mathematical ideas are triangle geometry with a 120° angular constraint, the Fermat (Fermat-Torricelli) point, and an optimization-by-comparison approach using distance sums. Construction workflow: Polygon and Line build the triangle ABC and the necessary connecting lines; Intersect determines key construction points; Angle is used to check the crucial 120° relationships; and Distance computes the lengths from constructed points to vertices (e.g., distanciaAA', distanciaBB', distanciaCC') with accompanying labels (TextoAA', TextoBB', TextoCC'). The script then forms SumaDistanciaVerticesF and compares it to SumaDistanciaVerticesP (and related text1) to visually confirm the minimum behavior. Suitable for advanced secondary students and introductory university learners studying geometric constructions, special points, and distance-sum minimization.