{"status": "success", "data": {"description_md": "Sides $\\overline{AB}$ and $\\overline{AC}$ of equilateral triangle $ABC$ are tangent to a circle at points $B$ and $C$ respectively.  What fraction of the area of $\\triangle ABC$ lies outside the circle?\n\n$\\textbf{(A)}\\ \\frac{4\\sqrt{3}\\pi}{27}-\\frac{1}{3}\\qquad\\textbf{(B)}\\ \\frac{\\sqrt{3}}{2}-\\frac{\\pi}{8}\\qquad\\textbf{(C)}\\ \\frac{1}{2}\\qquad\\textbf{(D)}\\ \\sqrt{3}-\\frac{2\\sqrt{3}\\pi}{9}\\qquad\\textbf{(E)}\\ \\frac{4}{3}-\\frac{4\\sqrt{3}\\pi}{27}$", "description_html": "<p>Sides  <span class=\"katex--inline\">\\overline{AB}</span>  and  <span class=\"katex--inline\">\\overline{AC}</span>  of equilateral triangle  <span class=\"katex--inline\">ABC</span>  are tangent to a circle at points  <span class=\"katex--inline\">B</span>  and  <span class=\"katex--inline\">C</span>  respectively.  What fraction of the area of  <span class=\"katex--inline\">\\triangle ABC</span>  lies outside the circle?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{4\\sqrt{3}\\pi}{27}-\\frac{1}{3}\\qquad\\textbf{(B)}\\ \\frac{\\sqrt{3}}{2}-\\frac{\\pi}{8}\\qquad\\textbf{(C)}\\ \\frac{1}{2}\\qquad\\textbf{(D)}\\ \\sqrt{3}-\\frac{2\\sqrt{3}\\pi}{9}\\qquad\\textbf{(E)}\\ \\frac{4}{3}-\\frac{4\\sqrt{3}\\pi}{27}</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": 4, "problem_name": "2017 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc10A_p23", "prev": "/problem/17_amc10A_p21"}}