Junior Mathematical Olympiad 2004 Section B Q14

In the square $ABCD$, $S$ is the point one quarter of the way from $A$ to $B$ and $T$ is the point one quarter of the way from $B$ to $A$. The points $U$, $V$, $W$, $X$, $Y$ and $Z$ are defined similarly. The eight points $S,T,U,V,W,X,Y,Z$ lie on a circle, whose centre is at the centre of the square. Determine which has the larger area: the square $ABCD$, or the circle.