Geometric Construction of Inscribed Sphere in a Cube

This GeoGebra example demonstrates how to construct a sphere inscribed in a cube. The core mathematical concepts include the spatial structure of cubes, the definition of inscribed spheres, point-line-plane positional relationships, and coordinate systems in 3D space. Construction steps: First, use the Cube command to create cube ABCD-EFGH, then use Midpoint to find midpoints of edges, create the sphere center using Point command, construct the sphere using Sphere command with radius equal to the distance from center to cube faces, and verify tangency using Intersect command. This example is suitable for secondary school solid geometry teaching, explaining inscribed and circumscribed sphere problems, and helping students understand spatial relationships between spheres and polyhedra.