T10.3.4 Tetrahedron in a sphere (sphere visible)
- Author:
- Emma Oates
Task 10.3.4
Imagine a tetrahedron contained in a sphere, seen as a large transparent balloon that just touches all four vertices of the tetrahedron that is trapped inside. Join each vertex of the tetrahedron to the midpoint of the opposite triangular face and extend this line out until it touches the sphere. This will give you four new points on the sphere. Imagine them as the vertices of a new tetrahedron. Describe to yourself how the two tetrahedra intersect.
Once you have finished the task, make a model and review your imaginings.