An equilateral triangle

- has two of its vertices below the \(x\)-axis,
- has the third vertex \(C\) above the \(x\)-axis, and
- contains \(A=(0,0)\) and \(B=(1,0)\) on its sides.

How long is the path traced out by all possible points \(C,\) to two decimal places?

If you think the path is infinitely long, provide 99999 as your answer. Or, if you think all the possible locations of \(C\) represent an area rather than a path, submit 99998 as your answer.

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