Tangent Plane and Tangent Line to a Sphere

① This example demonstrates the construction of a tangent plane to a sphere at a given point, and then the tangent line within that plane intersecting the sphere. ② Core mathematical concepts include the definition of a tangent plane to a sphere, the property that a tangent plane touches the sphere at exactly one point, and the relationship between lines in the tangent plane and the sphere (tangent lines). ③ Construction details: using GeoGebra commands Line, OrthogonalPlane, and Intersect; objects include points A, B, C, D, E, lines AB, b, d1, d2, and plane a. ④ Suitable for high school solid geometry or university analytic geometry courses, helping students visualize the construction and properties of tangent planes and lines, and enabling dynamic exploration as the point of tangency varies.