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$$R = \mbox{Area of quarter circle} - \mbox{Area of semicircle} - (\mbox{Area of semicircle} - B)$$ $$R = \frac{1}{4}\pi(2r)^2 - \frac{1}{2}\pi r^2 - \left(\frac{1}{2}\pi r^2 -B\right)$$ $$R = \pi r^2 - \frac{1}{2}\pi r^2 - \frac{1}{2}\pi r^2 +B$$ $$R=0+B$$ $$R=B$$

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