{"status": "success", "data": {"description_md": "Triangle $ABC$ is equilateral with $AB=1$. Points $E$ and $G$ are on $\\overline{AC}$ and points $D$ and $F$ are on $\\overline{AB}$ such that both $\\overline{DE}$ and $\\overline{FG}$ are parallel to $\\overline{BC}$. Furthermore, triangle $ADE$ and trapezoids $DFGE$ and $FBCG$ all have the same perimeter. What is $DE+FG$?<br><center><img class=\"problem-image\" alt='[asy] size(180); pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); real s=1/2,m=5/6,l=1; pair A=origin,B=(l,0),C=rotate(60)*l,D=(s,0),E=rotate(60)*s,F=m,G=rotate(60)*m; draw(A--B--C--cycle^^D--E^^F--G); dot(A^^B^^C^^D^^E^^F^^G); label(\"$A$\",A,SW); label(\"$B$\",B,SE); label(\"$C$\",C,N); label(\"$D$\",D,S); label(\"$E$\",E,NW); label(\"$F$\",F,S); label(\"$G$\",G,NW); [/asy]' class=\"latexcenter\" height=\"265\" src=\"https://latex.artofproblemsolving.com/d/2/e/d2eb992c9eae1b2af8bec0d92f03bde1e1e8b647.png\" width=\"302\"/></center>\n\n$\\textbf{(A) }1\\qquad<br>\\textbf{(B) }\\dfrac{3}{2}\\qquad<br>\\textbf{(C) }\\dfrac{21}{13}\\qquad<br>\\textbf{(D) }\\dfrac{13}{8}\\qquad<br>\\textbf{(E) }\\dfrac{5}{3}\\qquad$\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": "<p>Triangle  <span class=\"katex--inline\">ABC</span>  is equilateral with  <span class=\"katex--inline\">AB=1</span> . Points  <span class=\"katex--inline\">E</span>  and  <span class=\"katex--inline\">G</span>  are on  <span class=\"katex--inline\">\\overline{AC}</span>  and points  <span class=\"katex--inline\">D</span>  and  <span class=\"katex--inline\">F</span>  are on  <span class=\"katex--inline\">\\overline{AB}</span>  such that both  <span class=\"katex--inline\">\\overline{DE}</span>  and  <span class=\"katex--inline\">\\overline{FG}</span>  are parallel to  <span class=\"katex--inline\">\\overline{BC}</span> . Furthermore, triangle  <span class=\"katex--inline\">ADE</span>  and trapezoids  <span class=\"katex--inline\">DFGE</span>  and  <span class=\"katex--inline\">FBCG</span>  all have the same perimeter. What is  <span class=\"katex--inline\">DE+FG</span> ?<br/><center><img class=\"latexcenter\" alt=\"[asy] size(180); pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); real s=1/2,m=5/6,l=1; pair A=origin,B=(l,0),C=rotate(60)*l,D=(s,0),E=rotate(60)*s,F=m,G=rotate(60)*m; draw(A--B--C--cycle^^D--E^^F--G); dot(A^^B^^C^^D^^E^^F^^G); label(&#34;$A$&#34;,A,SW); label(&#34;$B$&#34;,B,SE); label(&#34;$C$&#34;,C,N); label(&#34;$D$&#34;,D,S); label(&#34;$E$&#34;,E,NW); label(&#34;$F$&#34;,F,S); label(&#34;$G$&#34;,G,NW); [/asy]\" height=\"265\" src=\"https://latex.artofproblemsolving.com/d/2/e/d2eb992c9eae1b2af8bec0d92f03bde1e1e8b647.png\" width=\"302\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }1\\qquad\\textbf{(B) }\\dfrac{3}{2}\\qquad\\textbf{(C) }\\dfrac{21}{13}\\qquad\\textbf{(D) }\\dfrac{13}{8}\\qquad\\textbf{(E) }\\dfrac{5}{3}\\qquad</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": "2013 AMC 12A Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12A_p12", "prev": "/problem/13_amc12A_p10"}}