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A triangle A B C is inscribed in a circl...

A triangle `A B C` is inscribed in a circle with centre at `O ,` The lines `A O ,B Oa n dC O` meet the opposite sides at `D , E ,a n dF ,` respectively. Prove that `1/(A D)+1/(B E)+1/(C F)=(acosA+bcosB+ccosC)/triangle`

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