# Problem #2127

 2127 In the figure, $\angle EAB$ and $\angle ABC$ are right angles. $AB=4, BC=6, AE=8$, and $AC$ and $BE$ intersect at $D$. What is the difference between the areas of $\triangle ADE$ and $\triangle BDC$? $[asy] unitsize(4mm); defaultpen(linewidth(.8pt)+fontsize(10pt)); pair A=(0,0), B=(4,0), C=(4,6), Ep=(0,8); pair D=extension(A,C,Ep,B); draw(A--C--B--A--Ep--B); label("A",A,SW); label("B",B,SE); label("C",C,N); label("E",Ep,N); label("D",D,2.5*N); label("4",midpoint(A--B),S); label("6",midpoint(B--C),E); label("8",(0,3),W); [/asy]$ $\mathrm{(A) \ } 2 \qquad \mathrm{(B) \ } 4 \qquad \mathrm{(C) \ } 5 \qquad \mathrm{(D) \ } 8 \qquad \mathrm{(E) \ } 9$ This problem is copyrighted by the American Mathematics Competitions.
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