2008 Cayley Problem 21

The circular window shown in the diagram has nine panes of equal area. The inner circular pane has radius 20 cm and the same centre, O, as the outer circle. The eight lines separating the outer panes are of equal length, x cm, and all, if extended, would pass through O. What is the value of x, to the nearest tenth?

\textbf{(A)}\ 40.0\quad \textbf{(B)}\ 36.6\quad \textbf{(C)}\ 30.0\quad \textbf{(D)}\ 20.0\quad \textbf{(E)}\ 43.2

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.