{"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 $ADEF$?
[asy] size(180); pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); real r=5/7; pair A=(10,sqrt(28^2-100)),B=origin,C=(20,0),D=(A.x*r,A.y*r); pair bottom=(C.x+(D.x-A.x),C.y+(D.y-A.y)); pair E=extension(D,bottom,B,C); pair top=(E.x+D.x,E.y+D.y); pair F=extension(E,top,A,C); draw(A--B--C--cycle^^D--E--F); dot(A^^B^^C^^D^^E^^F); label(\"$A$\",A,NW); label(\"$B$\",B,SW); label(\"$C$\",C,SE); label(\"$D$\",D,W); label(\"$E$\",E,S); label(\"$F$\",F,dir(0)); [/asy]
\n\n$\\textbf{(A) }48\\qquad
\\textbf{(B) }52\\qquad
\\textbf{(C) }56\\qquad
\\textbf{(D) }60\\qquad
\\textbf{(E) }72\\qquad$\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": "

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 ?

\"[asy]

\\textbf{(A) }48\\qquad\\textbf{(B) }52\\qquad\\textbf{(C) }56\\qquad\\textbf{(D) }60\\qquad\\textbf{(E) }72\\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2013 AMC 12A Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12A_p10", "prev": "/problem/13_amc12A_p08"}}