An triangle with sides 529 (red) and 128 (cyan) is inscribed in a circle (purple) of diameter 721. The length of the remaining longest side (black) in its simplest form can be represented as \(\frac{1}{721}\sqrt{a+b\sqrt{c}}\) where \(a,b\) and \(c\) are positive integers. Find \(a+b+c\).

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