Problem:
As shown below, convex pentagon has sides , , and . The pentagon is originally positioned in the plane with vertex at the origin and vertex on the positive -axis. The pentagon is then rolled clockwise to the right along the -axis. Which side will touch the point on the -axis?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Define a rotation of the pentagon to be a sequence that starts with on the -axis and ends when is on the -axis the first time thereafter. Because the pentagon has perimeter and , it follows that after rotations, point will be at and point will be at . Points and will next touch the -axis at and , respectively. Therefore a point on will touch .
The problems on this page are the property of the MAA's American Mathematics Competitions