Let \(\bigtriangleup ABC\) be an equilateral triangle inscribed in a circle. Let \(P\) be a point on the minor arc of \(BC\). If \(PB = 5000\) and \(PC = 346910923809328090099\). What is the length of \(AP\)?

**Note**: The numbers are indeed 5000 and 346910923809328090099.

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