Shortest Arc on a Sphere (Great Circle Minor Arc)

This GeoGebra example demonstrates the construction of the shortest path between two points on a sphere, which is the minor arc of the great circle passing through them. It illustrates the concept of geodesics on a spherical surface, emphasizing that the shortest arc lies on the intersection of the sphere with a plane through the sphere's center. The construction uses commands such as Sphere, PointIn, Point, Line, Plane, IntersectPath, CircumcircleArc, Tangent, OrthogonalLine, and Intersect to build the sphere, define points A and B, create the central plane, and generate the circular arc. Auxiliary tangents and intersection points help verify the minimality of the arc. This resource is suitable for high school or undergraduate students studying solid geometry, spherical trigonometry, or spatial analytic geometry, and serves as a visual aid for understanding geodesics and great-circle navigation.