1952 AMC 12 第 31 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
31.
平面内有 个点，其中任意三点不共线。这些点所确定的直线条数为：
Given points in a plane no three of which are collinear, the number of lines they determine is:
以上答案均不正确
None of these
小提示：
每条直线由这些点中的两个确定
Each line is determined by choosing two of the points
大提示：
任意三点不共线保证不同的点对确定不同的直线
The condition that no three are collinear ensures that different pairs determine different lines
解答：
每一对点确定一条直线；又因为任意三点不共线，所以没有一条直线会由多于一对点重复计数。因此，直线条数为
因此，正确答案是 D。
Every pair of points determines one line, and no line is counted by more than one pair because no three points are collinear. Therefore the number of lines is
Thus, the correct answer is D.