AMC 8 2003 Problem 22
Source:
July 23, 2011
geometryAMCAMC 8
Problem Statement
The following figures are composed of squares and circles. Which figure has a shaded region with largest area?
[asy]/* AMC8 2003 #22 Problem */
size(3inch, 2inch);
unitsize(1cm);
pen outline = black+linewidth(1);
filldraw((0,0)--(2,0)--(2,2)--(0,2)--cycle, mediumgrey, outline);
filldraw(shift(3,0)*((0,0)--(2,0)--(2,2)--(0,2)--cycle), mediumgrey, outline);
filldraw(Circle((7,1), 1), mediumgrey, black+linewidth(1));
filldraw(Circle((1,1), 1), white, outline);
filldraw(Circle((3.5,.5), .5), white, outline);
filldraw(Circle((4.5,.5), .5), white, outline);
filldraw(Circle((3.5,1.5), .5), white, outline);
filldraw(Circle((4.5,1.5), .5), white, outline);
filldraw((6.3,.3)--(7.7,.3)--(7.7,1.7)--(6.3,1.7)--cycle, white, outline);
label("A", (1, 2), N);
label("B", (4, 2), N);
label("C", (7, 2), N);
draw((0,-.5)--(.5,-.5), BeginArrow);
draw((1.5, -.5)--(2, -.5), EndArrow);
label("2 cm", (1, -.5));draw((3,-.5)--(3.5,-.5), BeginArrow);
draw((4.5, -.5)--(5, -.5), EndArrow);
label("2 cm", (4, -.5));draw((6,-.5)--(6.5,-.5), BeginArrow);
draw((7.5, -.5)--(8, -.5), EndArrow);
label("2 cm", (7, -.5));draw((6,1)--(6,-.5), linetype("4 4"));
draw((8,1)--(8,-.5), linetype("4 4"));[/asy]