Question

Assuming we have 4 line segments whose endpoints are on a circle, and all endpoints are unique. What is the maximum number of intersection points that can be formed from those intersecting segments?

A) 2 intersection points
B) 4 intersection points
C) 6 intersection points
D) 8 intersection points

Answer 1

The maximum number of intersection points that can be formed from 4 line segments on a circle is 8 intersection points.

Step-by-step explanation:

The maximum number of intersection points that can be formed from 4 line segments with unique endpoints on a circle is 8 intersection points.

1. Start by drawing out a circle and label four unique points/vertices along the circumference.
2. Now, connect these points with line segments to form a total of 4 line segments.
3. Using combinatorics, we can determine the number of intersection points. For each pair of line segments, there is exactly one intersection point. So, for 4 segments, the total number of intersection points is C(4,2) = 6. However, there are also two additional intersection points where three line segments intersect at a single point, resulting in a total of 8 intersection points.