ILL 1977 Problem 17

A ball $K$ of radius $r$ is touched from the outside by mutually equal balls of radius $R$ . Two of these balls are tangent to each other. Moreover, for two balls $K_1$ and $K_2$ tangent to $K$ and tangent to each other there exist two other balls tangent to $K_1,K_2$ and also to $K$ . How many balls are tangent to $K$ ? For a given $r$ determine $R$ .