# Kshitij's circumcircle

Geometry Level 4

In $$\Delta{ABC}$$,

$\overline{AB}^2+\overline{BC}^2+\overline{AC}^2 = \cos{A}\sin{B}\sin{C}+\sin{A}\cos{B}\sin{C}+\sin{A}\sin{B}\cos{C}.$

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


Note: This problem is posed by Kshitij J.

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