Circle and Sphere: Geometric Construction in 3D Space

① This example demonstrates the construction of a circle and a sphere in 3D space, showing their spatial relationships and geometric properties. ② Core mathematical concepts include the definition of a circle (set of points in a plane at a fixed distance from a center) and a sphere (set of points in space at a fixed distance from a center), as well as intersections and tangencies between points, lines, planes, and the sphere. ③ Construction highlights: Based on the summary, the example uses GeoGebra commands such as Sphere, Circle, Point, and Line, creating multiple points (A, B, C, D, E, F, G, etc.), lines (a, b, c, d, e, f, g, etc.), and objects like circles (c_1) and spheres (p, q, r, s, t). By dragging points or adjusting parameters, users can dynamically explore how the circle and sphere interact in different positions. ④ Suitable for high school solid geometry or college analytic geometry courses, this example helps students intuitively understand equations of circles and spheres, cross-sectional circles, center and radius, and serves as a teaching sample for 3D construction in GeoGebra.