Spherical Lines: Angles Formed by Great Circles

This GeoGebra example visualizes the angle between two great circles (AB and AC) on a sphere by drawing tangents to each circle at their intersection point A, converting the spherical angle into a planar angle. The core mathematical concept is spherical geometry: the angle between two curves on a sphere equals the angle between their tangents at the point of intersection. Construction steps include: using Sphere to create the sphere, PointIn to place points on the surface, Plane and IntersectPath to define great circles, Line and OrthogonalPlane to construct tangent lines, Circle and Intersect for auxiliary circles, and Angle to measure the angle α. Suitable for high school or university students learning solid geometry, spherical trigonometry, or spatial reasoning, and useful for teachers demonstrating the difference between spherical and planar angles.