VTRMC 2010 Problem 5

Let $A,B$ be two circles in the plane with $B$ inside $A$ . Assume that $A$ has radius $3$ , $B$ has radius $1$ , $P$ is a point on $A$ , $Q$ is a point on $B$ , and $A$ and $B$ touch so that $P$ and $Q$ are the same point. Suppose that $A$ is kept fixed and $B$ is rolled once round the inside of $A$ so that $Q$ traces out a curve starting and finishing at $P$ . What is the area enclosed by this curve?