2000 Cayley Problem 15

Eight squares with the same centre have parallel sides and are one unit apart. The two largest squares are shown. If the largest square has a perimeter of 96, what is the perimeter of the smallest square?

\textbf{(A)}\ 40\quad \textbf{(B)}\ 68\quad \textbf{(C)}\ 32\quad \textbf{(D)}\ 64\quad \textbf{(E)}\ 89

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.