2011 AMC 8 Problems/Problem 25

Problem

A circle with radius $1$ is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?

$[asy] filldraw((-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle,mediumgray,black); filldraw(Circle((0,0),1), mediumgray,black); filldraw((-1,0)--(0,1)--(1,0)--(0,-1)--cycle,white,black);[/asy]$

$\textbf{(A)}\ \frac{1}2\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ \frac{3}2\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \frac{5}2$

Solution

2011 AMC 8 (Problems • Answer Key • Resources)
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2011 AMC 8 Problems/Problem 25

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