# Product of Cosines

Geometry Level 4

Consider $$\Delta ABC$$ having semi-perimeter 21 and circumradius 8.125.

If $$\cos \dfrac{A}{2} \cos \dfrac{B}{2} \cos \dfrac{C}{2}$$ can be expressed as $$\dfrac{x}{y}$$ where $$x,y$$ are coprime positive integers, find $$x+y$$.

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