2002 AMC 8 第 1 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。
1.
在一张纸上画一个圆和两条不同的直线。这些图形最多可能有多少个交点？
A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures?
小提示：
分别数每一类图形对的交点。
Count each type of pair of figures separately.
大提示：
每条直线最多与圆相交两次，两条直线最多相交一次。
Each line can meet the circle at most twice, and the two lines can meet once.
解答：
一条直线和一个圆最多相交于两个点，两条不同直线最多相交于一个点。
安排两条直线都与圆相交两次，并且两条直线在另一个点相交。这样交点的总数为
所以正确答案是 D。
A line and a circle can intersect at no more than two points, and two distinct lines can intersect at no more than one point.
Arrange the two lines so each meets the circle twice and the two lines meet at a different point. This gives
Thus, D is the correct answer.
其他年份的第 1 题
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