{"status": "success", "data": {"description_md": "Let $ABCD$ be a square. Let $E, F, G$ and $H$ be the centers, respectively, of equilateral triangles with bases $\\overline{AB}, \\overline{BC}, \\overline{CD},$ and $\\overline{DA},$ each exterior to the square. What is the ratio of the area of square $EFGH$ to the area of square $ABCD$? \n\n$\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ \\frac{2+\\sqrt{3}}{3} \\qquad\\textbf{(C)}\\ \\sqrt{2} \\qquad\\textbf{(D)}\\ \\frac{\\sqrt{2}+\\sqrt{3}}{2} \\qquad\\textbf{(E)}\\ \\sqrt{3}$\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>Let  <span class=\"katex--inline\">ABCD</span>  be a square. Let  <span class=\"katex--inline\">E, F, G</span>  and  <span class=\"katex--inline\">H</span>  be the centers, respectively, of equilateral triangles with bases  <span class=\"katex--inline\">\\overline{AB}, \\overline{BC}, \\overline{CD},</span>  and  <span class=\"katex--inline\">\\overline{DA},</span>  each exterior to the square. What is the ratio of the area of square  <span class=\"katex--inline\">EFGH</span>  to the area of square  <span class=\"katex--inline\">ABCD</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ \\frac{2+\\sqrt{3}}{3} \\qquad\\textbf{(C)}\\ \\sqrt{2} \\qquad\\textbf{(D)}\\ \\frac{\\sqrt{2}+\\sqrt{3}}{2} \\qquad\\textbf{(E)}\\ \\sqrt{3}</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": "2016 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p18", "prev": "/problem/16_amc12A_p16"}}