{"status": "success", "data": {"description_md": "In the figure, $ABCD$ is a square of side length $1$. The rectangles $JKHG$ and $EBCF$ are congruent. What is $BE$?<br><center><img class=\"problem-image\" alt='[asy] pair A=(1,0), B=(0,0), C=(0,1), D=(1,1), E=(2-sqrt(3),0), F=(2-sqrt(3),1), G=(1,sqrt(3)/2), H=(2.5-sqrt(3),1), J=(.5,0), K=(2-sqrt(3),1-sqrt(3)/2); draw(A--B--C--D--cycle); draw(K--H--G--J--cycle); draw(F--E); label(\"$A$\",A,SE); label(\"$B$\",B,SW); label(\"$C$\",C,NW); label(\"$D$\",D,NE); label(\"$E$\",E,S); label(\"$F$\",F,N); label(\"$G$\",G,E); label(\"$H$\",H,N); label(\"$J$\",J,S); label(\"$K$\",K,W); [/asy]' class=\"latexcenter\" height=\"248\" src=\"https://latex.artofproblemsolving.com/2/b/c/2bcdf33d78300cd05d4666fa9c8ae141650dd693.png\" width=\"252\"/></center>\n\n$\\textbf{(A) }\\frac{1}{2}(\\sqrt{6}-2)\\qquad\\textbf{(B) }\\frac{1}{4}\\qquad\\textbf{(C) }2-\\sqrt{3}\\qquad\\textbf{(D) }\\frac{\\sqrt{3}}{6}\\qquad\\textbf{(E) } 1-\\frac{\\sqrt{2}}{2}$\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>In the figure,  <span class=\"katex--inline\">ABCD</span>  is a square of side length  <span class=\"katex--inline\">1</span> . The rectangles  <span class=\"katex--inline\">JKHG</span>  and  <span class=\"katex--inline\">EBCF</span>  are congruent. What is  <span class=\"katex--inline\">BE</span> ?<br/><center><img class=\"latexcenter\" alt=\"[asy] pair A=(1,0), B=(0,0), C=(0,1), D=(1,1), E=(2-sqrt(3),0), F=(2-sqrt(3),1), G=(1,sqrt(3)/2), H=(2.5-sqrt(3),1), J=(.5,0), K=(2-sqrt(3),1-sqrt(3)/2); draw(A--B--C--D--cycle); draw(K--H--G--J--cycle); draw(F--E); label(&#34;$A$&#34;,A,SE); label(&#34;$B$&#34;,B,SW); label(&#34;$C$&#34;,C,NW); label(&#34;$D$&#34;,D,NE); label(&#34;$E$&#34;,E,S); label(&#34;$F$&#34;,F,N); label(&#34;$G$&#34;,G,E); label(&#34;$H$&#34;,H,N); label(&#34;$J$&#34;,J,S); label(&#34;$K$&#34;,K,W); [/asy]\" height=\"248\" src=\"https://latex.artofproblemsolving.com/2/b/c/2bcdf33d78300cd05d4666fa9c8ae141650dd693.png\" width=\"252\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }\\frac{1}{2}(\\sqrt{6}-2)\\qquad\\textbf{(B) }\\frac{1}{4}\\qquad\\textbf{(C) }2-\\sqrt{3}\\qquad\\textbf{(D) }\\frac{\\sqrt{3}}{6}\\qquad\\textbf{(E) } 1-\\frac{\\sqrt{2}}{2}</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": 5, "problem_name": "2014 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12B_p22", "prev": "/problem/14_amc12B_p20"}}