Problem
2005 AMC 12A Problem 7
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}, E is between B and H, and BE = 1. What is the area of the inner square EFGH? ![[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]](/static/aops/b67d246a0ea0a1efc85e8d70586644afa3a3d2ad.png)
\textbf{(A) } 25 \qquad \textbf{(B) } 32 \qquad \textbf{(C) } 36 \qquad \textbf{(D) } 40 \qquad \textbf{(E) } 42
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