Fermat-Torricelli Point (Version 2): Constructing the Point Minimizing Sum of Di

This GeoGebra example demonstrates the construction of the Fermat-Torricelli point of a triangle, the point that minimizes the sum of distances to the three vertices. It visually shows that when all triangle angles are less than 120°, the Fermat point connects to the vertices with three 120° angles; otherwise, the obtuse vertex itself is the minimizer. Core mathematical concepts include triangle geometry, rotation, equilateral triangle construction, angle properties, and distance-sum optimization. The construction uses GeoGebra commands such as Segment, Polygon, Intersect, Point, and Angle. Key objects include the base triangle defined by points A, B, C, polygons poly1, poly2, poly3 formed by rotating sides to create equilateral triangles, and intersection points that lead to the Fermat point. This example is suitable for high school geometry, math competitions, or introductory university geometry, helping learners understand the existence and construction of the Fermat point and the power of rotation in solving geometric optimization problems.