OMM 2000 Problem 1

Circles $A,B,C,D$ are given on the plane such that circles $A$ and $B$ are externally tangent at $P, B$ and $C$ at $Q, C$ and $D$ at $R$ , and $D$ and $A$ at $S$ . Circles $A$ and $C$ do not meet, and so do not $B$ and $D$ . (a) Prove that the points $P,Q,R,S$ lie on a circle. (b) Suppose that $A$ and $C$ have radius $2, B$ and $D$ have radius $3$ , and the distance between the centers of $A$ and $C$ is $6$ . Compute the area of the quadrilateral $PQRS$ .