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.
by
Calvin Lin