AMC8 2002
AMC8 2002 · Q1
AMC8 2002 · Q1. It mainly tests Basic counting (rules of product/sum), Geometry misc.
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?
一张纸上画了一个圆和两条不同的直线。这些图形相交点的最大可能数量是多少？
(A)
2
2
(B)
3
3
(C)
4
4
(D)
5
5
(E)
6
6
Answer
Correct choice: (D)
正确答案：（D）
Solution
Two distinct lines can intersect in one point whereas a line can intersect a circle in two points. The maximum number 5 can be achieved if the lines and circle are arranged as shown. Note that the lines could also meet outside the circle for the same result. (Other arrangements of the lines and circle can produce 0, 1, 2, 3, or 4 points of intersection.)
两条不同的直线可以相交于一点，而一条直线可以与圆相交于两点。如果直线和圆按如图所示排列，可以实现最大数量5。注意，直线也可以在圆外相交，得到相同结果。（直线和圆的其他排列可以产生0、1、2、3或4个相交点。）
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