Problem

2004 AMC 10A Problem 9

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]

$\mathrm{(A) \ } 2 \qquad \mathrm{(B) \ } 4 \qquad \mathrm{(C) \ } 5 \qquad \mathrm{(D) \ } 8 \qquad \mathrm{(E) \ } 9$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

Show/Hide Problem Tags

Problem Tags: 2-d Geometry

Want to contribute problems and receive full credit? Click here to add your problem!
Please report any issues to us in our Discord server
Go to previous contest problem (SHIFT + Left Arrow) Go to next contest problem (SHIFT + Right Arrow)

Problem feedback

Difficulty —

Category: AMC 10A
Points: 1
Back to practice
Train more like this