{"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. <br>[[Image:2003amc10a19.gif]]\n\n$\\mathrm{(A) \\ } \\frac{1}{6}\\pi-\\frac{\\sqrt{3}}{4}\\qquad \\mathrm{(B) \\ } \\frac{\\sqrt{3}}{4}-\\frac{1}{12}\\pi\\qquad \\mathrm{(C) \\ } \\frac{\\sqrt{3}}{4}-\\frac{1}{24}\\pi\\qquad \\mathrm{(D) \\ } \\frac{\\sqrt{3}}{4}+\\frac{1}{24}\\pi\\qquad \\mathrm{(E) \\ } \\frac{\\sqrt{3}}{4}+\\frac{1}{12}\\pi$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A semicircle of diameter  <span class=\"katex--inline\">1</span>  sits at the top of a semicircle of diameter  <span class=\"katex--inline\">2</span> , as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is called a &#8216;&#8216;lune&#8217;&#8217;. Determine the area of this lune. <br/>[[Image:2003amc10a19.gif]]</p>&#10;<p> <span class=\"katex--inline\">\\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</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 12A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12A_p16", "prev": "/problem/03_amc12A_p14"}}