MathDB
Problem: 2004 AMC 10 #20

Source:

February 1, 2007
ratiogeometry

Problem Statement

Points EE and FF are located on square ABCDABCD so that ΔBEF\Delta BEF is equilateral. What is the ratio of the area of ΔDEF\Delta DEF to that of ΔABE\Delta ABE?
[asy] pair A=origin, B=(1,0), C=(1,1), D=(0,1), X=B+2*dir(165), E=intersectionpoint(B--X, A--D), Y=B+2*dir(105), F=intersectionpoint(B--Y, D--C); draw(B--C--D--A--B--F--E--B); pair point=(0.5,0.5); label("AA", A, dir(point--A)); label("BB", B, dir(point--B)); label("CC", C, dir(point--C)); label("DD", D, dir(point--D)); label("EE", E, dir(point--E)); label("FF", F, dir(point--F));[/asy]
<spanclass=latexbold>(A)</span>  43<spanclass=latexbold>(B)</span>  32<spanclass=latexbold>(C)</span>  3<spanclass=latexbold>(D)</span>  2<spanclass=latexbold>(E)</span>  1+3<span class='latex-bold'>(A)</span>\; \frac43\qquad <span class='latex-bold'>(B)</span>\; \frac32\qquad <span class='latex-bold'>(C)</span>\; \sqrt3\qquad <span class='latex-bold'>(D)</span>\; 2\qquad <span class='latex-bold'>(E)</span>\; 1+\sqrt3\qquad