# Sphere Inside Cube Inside Sphere

A sphere is inscribed in a cube such that it is tangent to all six faces (at their centers). This cube is also circumscribed by another sphere which intersects it at all eight vertices. What is the *square* of the ratio of the smaller sphere's radius to the radius of the larger sphere?

#### Attempt Info

- Correct Attempts: 25
- Incorrect Attempts: 32
- Ungraded Attempts: 0
- Total Attempts: 57