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 \(x+y\).


This problem is original.
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