Line-Sphere Intersections and Tangents

This example demonstrates the intersection points between a line and a sphere, the tangents at those points, and the relationship with the sphere's center. Key mathematical concepts include sphere equations, line equations, point-sphere relationships, and trigonometric applications. GeoGebra commands and objects used in construction are Sphere, Translate, points M, r_0, g, K_{Mr}, P_1, P_2, T, E1, E_1, h, M_k, r_k, u, u', v, v', T_1, T_2, g_T, Kr_k. Suitable for high school solid geometry teaching and learning, helping to understand spatial geometric relationships and calculations.