Two chords of a circle $\overline{PQ}$ and $\overline{RS}$ intersect at a point $O$. $\overline{PQ}$ is thrice as long as $\overline{RS}$. If $QO = 20$ and $RO = 10$, find the length of $\overline{PO}$.

Question

$\begin{array}{1 1} (a)\;20 \\ (b)\; 30 \\ (c)\; 60 \\ (d)\; \text{cannot be determined} \end{array}$