NL-NWO 2004 Problem 2

Two circles $A$ and $B$ , both with radius $1$ , touch each other externally. Four circles $P, Q, R$ and $S$ , all four with the same radius $r$ , lie such that $P$ externally touches on $A, B, Q$ and $S$ , $Q$ externally touches on $P, B$ and $R$ , $R$ externally touches on $A, B, Q$ and $S$ , $S$ externally touches on $P, A$ and $R$ . Calculate the length of $r.$