Question

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?

$2$

$3$

$4$

$5$

$6$

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。这样共有 $2+2+1=5$ 个交点。

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 $2+2+1=5.$

Thus, D is the correct answer.