2. Given a tetrahedron with three pairs of opposite edges of lengths $a$, $b$, and $c$, there is a sphere that is tangent to one face of the tetrahedron and the extensions of the other faces. Find the distance between the center of this sphere and the center of the tetrahedron's inscribed sphere.
Prompt Construct a rectangular parallelepiped such that the face diagonals of the parallelepiped are the edges of the original tetrahedron.

It can be proven: The vertices of the parallelepiped that are not vertices of the original tetrahedron are precisely the centers of a sphere that is tangent to one face of the tetrahedron and the extensions of the other faces.
The required distance is: $\frac{\sqrt{2}}{4} \sqrt{a^{2}+b^{2}+c^{2}}$.