# 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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