2009 Fermat Problem 20

In the diagram, the circle and the square have the same centre O and equal areas. The circle has radius 1 and intersects one side of the square at P and Q. What is the length of PQ?

\textbf{(A)}\ \sqrt{4-\pi}\quad \textbf{(B)}\ 1\quad \textbf{(C)}\ \sqrt{2}\quad \textbf{(D)}\ 2-\sqrt{\pi}\quad \textbf{(E)}\ 4-\sqrt{\pi}

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