A question says:
A sphere is inscribed in a regular tetrahedron. If the length of an altitude of the tetrahedron is 36, what is the length of a radius of the sphere?
I'm not sure where to start.
This is what I think so far:
- I think that the sphere touches the "center" of each of the tetrahedron's sides.
- Halfway down one of the tetrahedron's sides, where it meets the "altitude line" perpendicularly, is the radius of the sphere.
Apparently, the answer's 9.