{"status": "success", "data": {"description_md": "Points $E$ and $F$ are located on square $ABCD$ so that $\\triangle BEF$ is equilateral. What is the ratio of the area of $\\triangle DEF$ to that of $\\triangle ABE$?\n\n<center>\n<img class=\"problem-image\" height=\"185\" src=\"https://latex.artofproblemsolving.com/0/a/c/0acdbd9175edadf6ebc85fa2b0eaaaeb9737e067.png\" width=\"192\"/>\n</center>\n\n$\\mathrm{(A) \\ } \\frac{4}{3} \\qquad \\mathrm{(B) \\ } \\frac{3}{2} \\qquad \\mathrm{(C) \\ } \\sqrt{3} \\qquad \\mathrm{(D) \\ } 2 \\qquad \\mathrm{(E) \\ } 1+\\sqrt{3}$", "description_html": "<p>Points  <span class=\"katex--inline\">E</span>  and  <span class=\"katex--inline\">F</span>  are located on square  <span class=\"katex--inline\">ABCD</span>  so that  <span class=\"katex--inline\">\\triangle BEF</span>  is equilateral. What is the ratio of the area of  <span class=\"katex--inline\">\\triangle DEF</span>  to that of  <span class=\"katex--inline\">\\triangle ABE</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"185\" src=\"https://latex.artofproblemsolving.com/0/a/c/0acdbd9175edadf6ebc85fa2b0eaaaeb9737e067.png\" width=\"192\"/>\n</center>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{4}{3} \\qquad \\mathrm{(B) \\ } \\frac{3}{2} \\qquad \\mathrm{(C) \\ } \\sqrt{3} \\qquad \\mathrm{(D) \\ } 2 \\qquad \\mathrm{(E) \\ } 1+\\sqrt{3}</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": "2004 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10A_p21", "prev": "/problem/04_amc10A_p19"}}