{"status": "success", "data": {"description_md": "In $\\triangle ABC$, $AB=AC=28$ and $BC=20$.  Points $D,E,$ and $F$ are on sides $\\overline{AB}$, $\\overline{BC}$, and $\\overline{AC}$, respectively, such that $\\overline{DE}$ and $\\overline{EF}$ are parallel to $\\overline{AC}$ and $\\overline{AB}$, respectively.  What is the perimeter of parallelogram $ADEF$?\n\n<center>\n<img class=\"problem-image\" height=\"302\" src=\"https://latex.artofproblemsolving.com/e/c/4/ec45f0635e288a5e5da73a19319f4eb7045b5eab.png\" width=\"242\"/>\n</center>\n\n$\\textbf{(A) }48\\qquad\n\\textbf{(B) }52\\qquad\n\\textbf{(C) }56\\qquad\n\\textbf{(D) }60\\qquad\n\\textbf{(E) }72\\qquad$", "description_html": "<p>In  <span class=\"katex--inline\">\\triangle ABC</span> ,  <span class=\"katex--inline\">AB=AC=28</span>  and  <span class=\"katex--inline\">BC=20</span> .  Points  <span class=\"katex--inline\">D,E,</span>  and  <span class=\"katex--inline\">F</span>  are on sides  <span class=\"katex--inline\">\\overline{AB}</span> ,  <span class=\"katex--inline\">\\overline{BC}</span> , and  <span class=\"katex--inline\">\\overline{AC}</span> , respectively, such that  <span class=\"katex--inline\">\\overline{DE}</span>  and  <span class=\"katex--inline\">\\overline{EF}</span>  are parallel to  <span class=\"katex--inline\">\\overline{AC}</span>  and  <span class=\"katex--inline\">\\overline{AB}</span> , respectively.  What is the perimeter of parallelogram  <span class=\"katex--inline\">ADEF</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"302\" src=\"https://latex.artofproblemsolving.com/e/c/4/ec45f0635e288a5e5da73a19319f4eb7045b5eab.png\" width=\"242\"/>\n</center>\n<p> <span class=\"katex--inline\">\\textbf{(A) }48\\qquad\n\\textbf{(B) }52\\qquad\n\\textbf{(C) }56\\qquad\n\\textbf{(D) }60\\qquad\n\\textbf{(E) }72\\qquad</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": "2013 AMC 10A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc10A_p13", "prev": "/problem/13_amc10A_p11"}}