MathDB

9

Part of 2004 AMC 10

Problems(2)

Problem: 2004 AMC 10 #9

Source:

2/1/2007
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=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(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
geometry
Square and Circle

Source:

1/5/2009
A square has sides of length 10 10, and a circle centered at one of its vertices has radius 10 10. What is the area of the union of the regions enclosed by the square and the circle? (A)\ 200 \plus{} 25\pi\qquad (B)\ 100 \plus{} 75\pi\qquad (C)\ 75 \plus{} 100\pi\qquad (D)\ 100 \plus{} 100\pi (E)\ 100 \plus{} 125\pi
geometry