{"status": "success", "data": {"description_md": "Triangle $ABC$ has $AB=2 \\cdot AC$. Let $D$ and $E$ be on $\\overline{AB}$ and $\\overline{BC}$, respectively, such that $\\angle BAE = \\angle ACD$. Let $F$ be the intersection of segments $AE$ and $CD$, and suppose that $\\triangle CFE$ is equilateral. What is $\\angle ACB$?\n\n$\\textbf{(A)}\\ 60^\\circ \\qquad \\textbf{(B)}\\ 75^\\circ \\qquad \\textbf{(C)}\\ 90^\\circ \\qquad \\textbf{(D)}\\ 105^\\circ \\qquad \\textbf{(E)}\\ 120^\\circ$\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>Triangle  <span class=\"katex--inline\">ABC</span>  has  <span class=\"katex--inline\">AB=2 \\cdot AC</span> . Let  <span class=\"katex--inline\">D</span>  and  <span class=\"katex--inline\">E</span>  be on  <span class=\"katex--inline\">\\overline{AB}</span>  and  <span class=\"katex--inline\">\\overline{BC}</span> , respectively, such that  <span class=\"katex--inline\">\\angle BAE = \\angle ACD</span> . Let  <span class=\"katex--inline\">F</span>  be the intersection of segments  <span class=\"katex--inline\">AE</span>  and  <span class=\"katex--inline\">CD</span> , and suppose that  <span class=\"katex--inline\">\\triangle CFE</span>  is equilateral. What is  <span class=\"katex--inline\">\\angle ACB</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 60^\\circ \\qquad \\textbf{(B)}\\ 75^\\circ \\qquad \\textbf{(C)}\\ 90^\\circ \\qquad \\textbf{(D)}\\ 105^\\circ \\qquad \\textbf{(E)}\\ 120^\\circ</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": 2, "problem_name": "2010 AMC 12A Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p09", "prev": "/problem/10_amc12A_p07"}}