{"status": "success", "data": {"description_md": "Square $EFGH$ is inside the square $ABCD$ so that each side of $EFGH$ can be extended to pass through a vertex of $ABCD$. Square $ABCD$ has side length $\\sqrt {50}$ and $BE = 1$. What is the area of the inner square $EFGH$? <br><center><img class=\"problem-image\" alt='[asy] unitsize(4cm); defaultpen(linewidth(.8pt)+fontsize(10pt)); pair D=(0,0), C=(1,0), B=(1,1), A=(0,1); pair F=intersectionpoints(Circle(D,2/sqrt(5)),Circle(A,1))[0]; pair G=foot(A,D,F), H=foot(B,A,G), E=foot(C,B,H); draw(A--B--C--D--cycle); draw(D--F); draw(C--E); draw(B--H); draw(A--G); label(\"$A$\",A,NW); label(\"$B$\",B,NE); label(\"$C$\",C,SE); label(\"$D$\",D,SW); label(\"$E$\",E,NNW); label(\"$F$\",F,ENE); label(\"$G$\",G,SSE); label(\"$H$\",H,WSW); [/asy]' class=\"latexcenter\" height=\"225\" src=\"https://latex.artofproblemsolving.com/6/3/9/63933d5d224cb8b1a275205d6c3c0baab193dd47.png\" width=\"228\"/></center>\n\n$(\\mathrm {A}) \\ 25 \\qquad (\\mathrm {B}) \\ 32 \\qquad (\\mathrm {C})\\ 36 \\qquad (\\mathrm {D}) \\ 40 \\qquad (\\mathrm {E})\\ 42$\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>Square  <span class=\"katex--inline\">EFGH</span>  is inside the square  <span class=\"katex--inline\">ABCD</span>  so that each side of  <span class=\"katex--inline\">EFGH</span>  can be extended to pass through a vertex of  <span class=\"katex--inline\">ABCD</span> . Square  <span class=\"katex--inline\">ABCD</span>  has side length  <span class=\"katex--inline\">\\sqrt {50}</span>  and  <span class=\"katex--inline\">BE = 1</span> . What is the area of the inner square  <span class=\"katex--inline\">EFGH</span> ? <br/><center><img class=\"latexcenter\" alt=\"[asy] unitsize(4cm); defaultpen(linewidth(.8pt)+fontsize(10pt)); pair D=(0,0), C=(1,0), B=(1,1), A=(0,1); pair F=intersectionpoints(Circle(D,2/sqrt(5)),Circle(A,1))[0]; pair G=foot(A,D,F), H=foot(B,A,G), E=foot(C,B,H); draw(A--B--C--D--cycle); draw(D--F); draw(C--E); draw(B--H); draw(A--G); label(&#34;$A$&#34;,A,NW); label(&#34;$B$&#34;,B,NE); label(&#34;$C$&#34;,C,SE); label(&#34;$D$&#34;,D,SW); label(&#34;$E$&#34;,E,NNW); label(&#34;$F$&#34;,F,ENE); label(&#34;$G$&#34;,G,SSE); label(&#34;$H$&#34;,H,WSW); [/asy]\" height=\"225\" src=\"https://latex.artofproblemsolving.com/6/3/9/63933d5d224cb8b1a275205d6c3c0baab193dd47.png\" width=\"228\"/></center></p>&#10;<p> <span class=\"katex--inline\">(\\mathrm {A}) \\ 25 \\qquad (\\mathrm {B}) \\ 32 \\qquad (\\mathrm {C})\\ 36 \\qquad (\\mathrm {D}) \\ 40 \\qquad (\\mathrm {E})\\ 42</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": "2005 AMC 12A Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc12A_p08", "prev": "/problem/05_amc12A_p06"}}