AMC 8 1986 Problem 23

AMC8 1986 年第 23 题

圆★★★★☆

The large circle has diameter

\textAC

. The two small circles have their centers on

\textAC

and just touch at

\textO

, the center of the large circle. If each small circle has radius 1, what is the value of the ratio of the area of the shaded region to the area of one of the small circles?

大圆的直径为

\textAC

。两个小圆的圆心在

\textAC

上，且恰好在

\textO

点（大圆的圆心）相切。如果每个小圆的半径为 1，着色区域与一个小圆的面积之比是多少？

A. $\displaystyle \text{between }\frac{1}{2}\text{ and 1}$
B.1
C. $\displaystyle \text{between 1 and }\frac{3}{2}$

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