ILL 1976 Problem 22

A regular pentagon $A_1A_2A_3A_4A_5$ with side length $s$ is given. At each point $A_i$ , a sphere $K_i$ of radius $\frac{s}{2}$ is constructed. There are two spheres $K_1$ and $K_2$ each of radius $\frac{s}{2}$ touching all the five spheres $K_i.$ Decide whether $K_1$ and $K_2$ intersect each other, touch each other, or have no common points.