Absolutely geometric

Geometry Level pending

In triangle \(PQR\), the respective length of the sides \(PQ\) and \(PR\) are denoted by \(u\) and \(v\) while the length of the median \(PS\) is denoted by \(w\). It is known that \(w\) is the geometric mean of \(u\) and \(v\), and \(\angle QPR = 60\).

The value of \(|\cos(\angle PQR) - \cos(\angle QRP) | = \dfrac{a}{b\sqrt{c}}\), where \(|x|\) denotes the absolute value of \(x\).

Then find the value of \(a+b+c \)

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