A regular tetrahedron $s$ contains three spheres. The first sphere passes through the vertices of the tetrahedron, the second through the midpoints of the edges; the third touches the faces of the tetrahedron. How do the surface areas of these spheres relate to each other?
The radii of the spheres are respectively: $\frac{a}{4} \sqrt{6}, \frac{a}{4} \sqrt{2}, \frac{a}{12} \sqrt{6}$; the surfaces of the spheres are in the same ratio as the squares of their radii, that is,

$$
9: 3: 1
$$

The problem was solved by: Czank K., Deutsch N., Freibauer E., Kiss A., Kohn B., Krisztián Gy., Lukhaub Gy., Scholtz G., Tinyó J., Weisz J.