{"status": "success", "data": {"description_md": "A circle of radius 2 is centered at $A$. An equilateral triangle with side 4 has a vertex at $A$. What is the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle?\n\n$\\textbf{(A)}\\; 8-\\pi \\qquad\\textbf{(B)}\\; \\pi+2 \\qquad\\textbf{(C)}\\; 2\\pi-\\dfrac{\\sqrt{2}}{2} \\qquad\\textbf{(D)}\\; 4(\\pi-\\sqrt{3}) \\qquad\\textbf{(E)}\\; 2\\pi-\\dfrac{\\sqrt{3}}{2}$\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 circle of radius 2 is centered at  <span class=\"katex--inline\">A</span> . An equilateral triangle with side 4 has a vertex at  <span class=\"katex--inline\">A</span> . What is the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\; 8-\\pi \\qquad\\textbf{(B)}\\; \\pi+2 \\qquad\\textbf{(C)}\\; 2\\pi-\\dfrac{\\sqrt{2}}{2} \\qquad\\textbf{(D)}\\; 4(\\pi-\\sqrt{3}) \\qquad\\textbf{(E)}\\; 2\\pi-\\dfrac{\\sqrt{3}}{2}</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": "2015 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12B_p15", "prev": "/problem/15_amc12B_p13"}}