\(ABCD\) is a square with side length \(10\) and \(P\) is a point in the interior of \(ABCD\) such that \(PA=6\) and \(PB=8\). If the length of \(PC\) is written as \(a\sqrt{b}\), where \(a\) and \(b\) are positive integers, and \(b\) is not a multiple of the square of any prime, what is the value of \(a+b\)?

This problem is posed by Qi Huan T.

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