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jmc

algebra junior

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?

Enter "AB", "BC", "CD", "DE", or "EA".

problem
Solution
Side covers the interval then covers the interval then covers the interval then covers the interval then covers the interval and then the process repeats. The intervals the sides touch repeat with period 23.

Since side touches the point 2009.
Final answer
\overline{CD}