AHSME 1980 Problem 26

Four balls of radius $1$ are mutually tangent, three resting on the floor and the fourth resting on the others. A tetrahedron, each of whose edges have length $s$, is circumscribed around the balls. Then $s$ equals $\text{(A)} \ 4\sqrt 2 \text{(B)} \ 4\sqrt 3 \text{(C)} \ 2\sqrt 6 \text{(D)}\ 1+2\sqrt 6 \text{(E)}\ 2+2\sqrt 6$