MathDB
Problem: 2004 AMC 10 #9

Source:

February 1, 2007
geometry

Problem Statement

In the figure, EAB \angle EAB and ABC \angle ABC are right angles. AB \equal{} 4, BC \equal{} 6, AE \equal{} 8, and AC \overline{AC} and BE \overline{BE} intersect at D D. What is the difference between the areas of ADE \triangle ADE and BDC \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("AA",A,SW); label("BB",B,SE); label("CC",C,N); label("EE",Ep,N); label("DD",D,2.5*N); label("44",midpoint(A--B),S); label("66",midpoint(B--C),E); label("88",(0,3),W);[/asy]<spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 5<spanclass=latexbold>(D)</span> 8<spanclass=latexbold>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 2\qquad <span class='latex-bold'>(B)</span>\ 4\qquad <span class='latex-bold'>(C)</span>\ 5\qquad <span class='latex-bold'>(D)</span>\ 8\qquad <span class='latex-bold'>(E)</span>\ 9