Extended Bisector

Geometry Level 3

Triangle \(ABC\) is inscribed in a unit circle. The three bisectors of the angle \(A\), \(B\) and \(C\) are extended to intersect the circle at \(A'\), \(B'\) and \(C'\) respectively. Determine the value of

\[\frac{AA'\cos\frac{A}{2}+BB'\cos\frac{B}{2}+CC'\cos\frac{C}{2}}{\sin A+\sin B+\sin C}\]

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