Fermat Point (Punto de Fermat) Geometric Construction

This example demonstrates the geometric construction of the Fermat point of a triangle, which is the point inside the triangle that minimizes the sum of distances to the three vertices. Core mathematical concepts include triangles, line segments, circles, intersections, polygons, midpoints, angles, and symmetry. The construction uses GeoGebra commands such as Segment, Circle, Intersect, Polygon, Midpoint, and Angle, along with multiple auxiliary objects (e.g., P_1, P_2, P_3, I_0, m_1, m_2, m_3, c_1) to build equilateral triangles and auxiliary circles, ultimately determining the Fermat point F. This example is suitable for high school or college geometry courses to understand the existence, construction, and relationship of the Fermat point to triangle angles, and also for exploring optimization problems.