{"status": "success", "data": {"description_md": "The figure shown is called a ''trefoil'' and is constructed by drawing circular sectors about the sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length $2$?\n\n<center>\n<img class=\"problem-image\" height=\"148\" src=\"https://latex.artofproblemsolving.com/a/d/d/add63d336a5010d8962e6c449e606e802e144685.png\" width=\"145\"/>\n</center>\n\n$\\mathrm{(A) \\ } \\frac{1}{3}\\pi+\\frac{\\sqrt{3}}{2}\\qquad \\mathrm{(B) \\ } \\frac{2}{3}\\pi\\qquad \\mathrm{(C) \\ } \\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{4}\\qquad \\mathrm{(D) \\ } \\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{3}\\qquad \\mathrm{(E) \\ } \\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{2}$", "description_html": "<p>The figure shown is called a &#8220;trefoil&#8221; and is constructed by drawing circular sectors about the sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length  <span class=\"katex--inline\">2</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"148\" src=\"https://latex.artofproblemsolving.com/a/d/d/add63d336a5010d8962e6c449e606e802e144685.png\" width=\"145\"/>\n</center>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{1}{3}\\pi+\\frac{\\sqrt{3}}{2}\\qquad \\mathrm{(B) \\ } \\frac{2}{3}\\pi\\qquad \\mathrm{(C) \\ } \\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{4}\\qquad \\mathrm{(D) \\ } \\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{3}\\qquad \\mathrm{(E) \\ } \\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{2}</span> </p>\n<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": "2005 AMC 10A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10A_p13", "prev": "/problem/05_amc10A_p11"}}