2
$\begingroup$

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.

5 Answers 5