Sphere-Related Circle Intersections with Conditional Geometry

This example demonstrates a 3D geometry construction where sphere-related circle/plane relationships are combined with conditional constraints to visualize intersection points and intersection paths. The key mathematical ideas include solid geometry concepts (spatial relationships among a sphere, planes, and circle-like features), the use of “point in” logic to determine whether a point satisfies a geometric condition, and intersection computations between constructed objects to obtain the resulting configuration. Construction highlights from the provided GeoGebra summary: PointIn is used to test point objects against the relevant geometric condition (e.g., belonging to/lying on the intended locus or surface relation); Plane is used to create the constraint plane(s) that guide the configuration; and IntersectPath is used to compute or trace the intersection path produced by the interacting objects under those constraints. The involved objects (r, vgl1, vgl2, A, p, c, O, B, q, d) correspond to the sphere/circle-like elements, reference points in space, and auxiliary parameters/directions that define the conditional geometry and drive the final intersection structure. Suitable for upper secondary to early university students for solid-geometry visualization, geometric construction practice, and interactive teaching of 3D intersection concepts.