# 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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