Australian AMC 2008 - Intermediate Question 19

Question 19

$PR$ and $QS$ are perpendicular diameters drawn on a circle centre $O$. The points $T,U,V$ and $W$ are the midpoints of $PO,QO,RO$ and $SO$ respectively.

The fraction of the circle covered by the shaded area is

Question illustration

$\frac1{2\pi}$
$\frac1\pi$
$\frac3{2\pi}$
$\frac2\pi$
$\frac5{2\pi}$