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Arc  $$AC$$is a quarter-circle with center $$B$$. The shaded region $$ABC$$ is "rolled" along a straight board $$PQ$$ until it reaches its original orientation for the first time with point $$B$$ landing at point $$B'$$. If  $$BC = 2/\pi$$ cm, what is the length of the path that point $$B$$ travels? Express your answer in simplest form.

Dec 30, 2021