MathDB

22

Part of 1987 AMC 8

Problems(1)

1987 AJHSME Problem 22

Source:

6/25/2011
ABCD\text{ABCD} is a rectangle, D\text{D} is the center of the circle, and B\text{B} is on the circle. If AD=4\text{AD}=4 and CD=3\text{CD}=3, then the area of the shaded region is between
[asy] pair A,B,C,D; A=(0,4); B=(3,4); C=(3,0); D=origin; draw(circle(D,5)); fill((0,5)..(1.5,4.7697)..B--A--cycle,black); fill(B..(4,3)..(5,0)--C--cycle,black); draw((0,5)--D--(5,0)); label("A",A,NW); label("B",B,NE); label("C",C,S); label("D",D,SW); [/asy]
(A) 4 and 5(B) 5 and 6(C) 6 and 7(D) 7 and 8(E) 8 and 9\text{(A)}\ 4\text{ and }5 \qquad \text{(B)}\ 5\text{ and }6 \qquad \text{(C)}\ 6\text{ and }7 \qquad \text{(D)}\ 7\text{ and }8 \qquad \text{(E)}\ 8\text{ and }9
geometryrectangle