2001 AMC 10 第 4 题

Question

一个圆和一个三角形最多可能有多少个交点？

What is the maximum number of possible points of intersection of a circle and a triangle?

2

3

4

5

6

一条直线最多与一个圆相交于

2

个点。

A line can cross a circle in at most

2

points

一个三角形有

3

条边。

A triangle has

3

sides

三角形的每条边都是线段，最多与圆相交于

2

个点；三角形有

3

条边，所以最多有

3\cdot2=6

个交点，而且这个上界可以达到。

所以正确答案是 E。

Each side of the triangle is a segment, which can intersect a circle in at most

2

points. With

3

sides, the maximum is

3\cdot2=6

points, and this is achievable.

Thus, the correct answer is E.

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