Intersection of a Cone and a Sphere

This GeoGebra example demonstrates the geometric intersection of a cone and a sphere in three-dimensional space, visualizing the spatial curve formed by their intersection. Core mathematical concepts include solid geometry, surface intersections, spatial loci, tangent properties, and geometric symmetries (such as isosceles and rhombic cross-sections). To construct this model, the GeoGebra commands Cone and Sphere are used to define the primary 3D shapes, Line is used for auxiliary construction lines, and Intersect along with IntersectPath are crucial for calculating the intersection points and the continuous intersection path. The construction involves key parameters and objects such as r2, r1, a, c, d, r, j, m, M, N, b, e, f, g, h, A, and B. This example is highly suitable for high school or college-level solid geometry and spatial analytic geometry courses, serving as a visual teaching tool for understanding complex spatial intersections.