Problem:
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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Two distinct lines can intersect in one point whereas a line can intersect a circle in two points. The maximum number can be achieved if the lines and circle are arranged as shown. Note that the lines could also meet outside the circle for the same result. (Other arrangements of the lines and circle can produce , or points of intersection.)
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions