1950 AMC 12 第 45 题

Question

一个

100

边形可以画出的对角线条数为：

The number of diagonals that can be drawn in a polygon of

100

sides is:

4850

4950

9900

98

8800

每一对顶点确定一条线段

Every pair of vertices determines a segment

从

\binom{100}{2}

对顶点中减去

100

条边

Subtract the

100

sides from the

\binom{100}{2}

vertex pairs

连接各对顶点共有

\binom{100}{2}

条线段，其中恰有

100

条是多边形的边，所以对角线条数为

\begin{aligned} \binom{100}{2}-100 &=4950-100\\ &=4850 \end{aligned}\text{。}

因此，正确答案是 A。

There are

\binom{100}{2}

segments joining pairs of vertices. Exactly

100

of these are sides, so the number of diagonals is

\begin{aligned} \binom{100}{2}-100 &=4950-100\\ &=4850. \end{aligned}

Thus, the correct answer is A.

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