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8. (20 points (bonus)) Here n bugs are placed at the vertices of a regular n-gon with side length a. The bugs crawl counterclockwise at the same speed and each bug crawls directly toward the next bug at all times. They approach the center of the a-gon along spiral paths. The figure below shows the case where n = 5 (a) (10 points) Find the polar equation of a bug's path assuming the pole is at the center of the n-gon. (Use the fact that the line joining one bug to the next is tangent to the bug's path.) (b) (10 points) Find the distance traveled by a bug by the time it meets the other bugs at the center