$\frac{PT}{ST}=\frac{1}{6}$
$ST=6k, OT=3k\therefore OP=2K$
$\angle AOP=30^{\circ}$ $\because sin30^{\circ} =\frac{1}{2}$
$AO=\sqrt{3}k$และ$\angle APO=60^{\circ} $
$\therefore$พ.ท.แรเงา$=2[(\frac{1}{2}\sqrt{3}k^2)-\frac{1}{6}\pi k^2]$
$\quad\quad\quad=(\sqrt{3}-\frac{\pi }{3})k^2$