【Analysis】Since two points determine a line segment, and because no three points are collinear, any three points can form a triangle. Assuming three of the points are connected to form a triangle, to minimize the number of intersections of these line segments, the remaining two points should be inside the triangle. According to this, draw the diagram to solve the problem.

【Solution】Solution: According to the analysis of the problem, the diagram is drawn as follows:
Answer: There is at least 1 intersection point.
Therefore, the answer is: 1.
8. (10 points) In a plane, there are 5 points, among which no 3 points are collinear. Connecting line segments with these points as endpoints, apart from these 5 points, these line segments have at least $\qquad$ intersection points.