{"status": "success", "data": {"description_md": "A semicircle of diameter $1$ sits at the top of a semicircle of diameter $2$, as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is called a ''lune''. Determine the area of this lune. \n\n
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\n\n$\\mathrm{(A) \\ } \\frac{1}{6}\\pi-\\frac{\\sqrt{3}}{4}\\qquad \\mathrm{(B) \\ } \\frac{\\sqrt{3}}{4}-\\frac{1}{12}\\pi\\qquad \\mathrm{(C) \\ } \\frac{\\sqrt{3}}{4}-\\frac{1}{24}\\pi\\qquad \\mathrm{(D) \\ } \\frac{\\sqrt{3}}{4}+\\frac{1}{24}\\pi\\qquad \\mathrm{(E) \\ } \\frac{\\sqrt{3}}{4}+\\frac{1}{12}\\pi$", "description_html": "

A semicircle of diameter 1 sits at the top of a semicircle of diameter 2 , as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is called a “lune”. Determine the area of this lune.

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\\mathrm{(A) \\ } \\frac{1}{6}\\pi-\\frac{\\sqrt{3}}{4}\\qquad \\mathrm{(B) \\ } \\frac{\\sqrt{3}}{4}-\\frac{1}{12}\\pi\\qquad \\mathrm{(C) \\ } \\frac{\\sqrt{3}}{4}-\\frac{1}{24}\\pi\\qquad \\mathrm{(D) \\ } \\frac{\\sqrt{3}}{4}+\\frac{1}{24}\\pi\\qquad \\mathrm{(E) \\ } \\frac{\\sqrt{3}}{4}+\\frac{1}{12}\\pi

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 10A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10A_p20", "prev": "/problem/03_amc10A_p18"}}