Algebraic Determination of the Fermat-Torricelli Point

This GeoGebra example demonstrates how to use algebraic methods to determine the Fermat-Torricelli point (Fermat point) in a triangle. The Fermat point is the special point inside a triangle that minimizes the sum of distances to the three vertices. Core mathematical concepts include: Fermat point theory (when all interior angles of a triangle are less than 120°, the Fermat point satisfies that the angles between any two connecting segments to the vertices are all 120°), trigonometry, area methods, and equation solving. Construction details: Use Polygon command to draw triangle ABC, use Line and Angle commands to construct 120° angle lines, use Intersect command to find the intersection point (Fermat point F), use Segment command to measure distances and verify that AF+BF+CF is minimized. Suitable for high school mathematics electives and geometry competition training, helpful for understanding the connection between optimization problems and geometric construction.