Problem: Convex polygons and are drawn in the same plane with and sides, respectively, . If and do not have any line segment in common, then the maximum number of intersections of and is:
Answer Choices:
A.
B.
C.
D.
E. none of these
Solution:
Each side of can fail to enter the boundary or interior of , or it can enter and terminate, or it can continue on to the exterior. Therefore, at most, each side of meets two sides of , so that the maximum number of intersections is . This maximum is attained as follows:
