Kshitij's circumcircle

Geometry Level 4

In ΔABC\Delta{ABC},

AB2+BC2+AC2=cosAsinBsinC+sinAcosBsinC+sinAsinBcosC.\overline{AB}^2+\overline{BC}^2+\overline{AC}^2 = \cos{A}\sin{B}\sin{C}+\sin{A}\cos{B}\sin{C}+\sin{A}\sin{B}\cos{C}.

If the area of the circumcircle of ΔABC\Delta{ABC} can be represented as aπb\frac{a\pi}{b}, where aa and bb are coprime positive integers, what is the value of a+b?a+b?


Note: This problem is posed by Kshitij J.

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