AMC 8 2012 Problem 24

AMC8 2012 年第 24 题

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A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?

半径为 2 的圆被分割成 4 段相等的弧，这 4 段弧拼接成如图所示的星型。那么这个星型的面积和原来圆的面积的比值是多少？

AMC 8 2012 Problem 24 figure

A. $\displaystyle \hspace{.05in}\frac{4-\pi}{\pi}$
B. $\displaystyle \hspace{.05in}\frac{1}\pi$
C. $\displaystyle \hspace{.05in}\frac{\sqrt2}{\pi}$
D. $\displaystyle \hspace{.05in}\frac{\pi-1}{\pi}$
E. $\displaystyle \hspace{.05in}\frac{3}\pi$

正确答案 · Correct Answer

A

解析 · Solution

解析整理中

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