An equilateral triangle, ABC, has two of its vertices, A and B, below the x-axis

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An equilateral triangle, ABC, has two of its vertices, A and B, below
the x-axis; has the third vertex C above the x-axis, and contains the
points (0,0) on segment AC, and (0,1) on segment BC. How long is the
path traced out by all possible points C to two decimal places?

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