1960 AMC 12 第 6 题

Question

一个圆的周长为

100

英寸。该圆内接正方形的边长（以英寸计）是：

The circumference of a circle is

100

inches. The side of a square inscribed in this circle, expressed in inches, is:

\dfrac{25\sqrt2}{\pi}

\dfrac{50\sqrt2}{\pi}

\dfrac{100}{\pi}

\dfrac{100\sqrt2}{\pi}

50\sqrt2

由周长求出直径

Find the diameter from the circumference

内接正方形的对角线就是圆的直径

The diagonal of the inscribed square is the circle’s diameter

直径为

\frac{100}{\pi}

。若正方形的边长为

s

，则其对角线为

s\sqrt2

，所以

s\sqrt2=\frac{100}{\pi}\text{。}

因此

s=\frac{50\sqrt2}{\pi}

。

因此，正确答案是 B。

The diameter is

\frac{100}{\pi}.

If the square has side

s,

its diagonal is

s\sqrt2,

so

s\sqrt2=\frac{100}{\pi}.

Therefore

s=\frac{50\sqrt2}{\pi}.

Thus, the correct answer is B.

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