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CEMC Gauss (Grade 8), 2010

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

Two circles each have radius $10$ cm. They overlap so that each contains exactly $25\%$ of the other's circumference, as shown. The area of the shaded region is closest to

(A) $57.08\text{ cm}^2$ (B) $55.24\text{ cm}^2$ (C) $51.83\text{ cm}^2$ (D) $54.17\text{ cm}^2$ (E) $53.21\text{ cm}^2$

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