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In rectangle $ABCD,$ corner $A$ is folded over crease $\overline{DE}$ to point $F$ on $\overline{BC}.$ Find $BC.$

[asy] unitsize(1 cm);pair A, B, C, D, E, F;A = (0,3);B = (0,0);C = (5,0);D = (5,3);F = (1,0);E = extension((A + F)/2, (A + F)/2 + rotate(90)*(F - A), A, B);draw(E--A--D,dashed);draw(B--E--D--C--cycle);draw(E--F--D);label(

 Apr 3, 2022
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BC = 10*sqrt(3).

 Apr 3, 2022

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