Extended Bisector

Geometry Level 3

Triangle ABCABC is inscribed in a unit circle. The three bisectors of the angle AA, BB and CC are extended to intersect the circle at AA', BB' and CC' respectively. Determine the value of

AAcosA2+BBcosB2+CCcosC2sinA+sinB+sinC\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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