{"status": "success", "data": {"description_md": "The closed curve in the figure is made up of $9$ congruent circular arcs each of length $\\frac{2\\pi}{3}$, where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side $2$. What is the area enclosed by the curve?\n\n<center>\n<img class=\"problem-image\" height=\"245\" src=\"https://latex.artofproblemsolving.com/c/4/3/c431f575740b9b695b706edb44a2fbc2971431e3.png\" width=\"262\"/>\n</center><br>\n\n$\\textbf{(A)}\\ 2\\pi+6\\qquad\\textbf{(B)}\\ 2\\pi+4\\sqrt{3}\\qquad\\textbf{(C)}\\ 3\\pi+4\\qquad\\textbf{(D)}\\ 2\\pi+3\\sqrt{3}+2\\qquad\\textbf{(E)}\\ \\pi+6\\sqrt{3}$", "description_html": "<p>The closed curve in the figure is made up of <span class=\"katex--inline\">9</span> congruent circular arcs each of length <span class=\"katex--inline\">\\frac{2\\pi}{3}</span>, where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side <span class=\"katex--inline\">2</span>. What is the area enclosed by the curve?</p>&#10;<center>&#10;<img class=\"problem-image\" height=\"245\" src=\"https://latex.artofproblemsolving.com/c/4/3/c431f575740b9b695b706edb44a2fbc2971431e3.png\" width=\"262\"/>&#10;</center><br/>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 2\\pi+6\\qquad\\textbf{(B)}\\ 2\\pi+4\\sqrt{3}\\qquad\\textbf{(C)}\\ 3\\pi+4\\qquad\\textbf{(D)}\\ 2\\pi+3\\sqrt{3}+2\\qquad\\textbf{(E)}\\ \\pi+6\\sqrt{3}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2012 AMC 10A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc10A_p19", "prev": "/problem/12_amc10A_p17"}}