AMC10每日一题（2001年真题#04）

2001 AMC 10 竞赛试题/第04题

Problem

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

Solution

Solution 1

We can draw a circle and a triangle, such that each side is tangent to the circle. This means that each side would intersect the circle at one point.

You would then have  points, but what if the circle was bigger? Then, each side would intersect the circle at 2 points.

Therefore, .

Solution 2

We know that the maximum amount of points that a circle and a line segment can intersect is . Therefore, because there are  line segments in a triangle, the maximum amount of points of intersection is .