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If ´ O ´ is the circumcentre of increment A B C blankandblank R subscript 1 end subscript comma R subscript 2 end subscript blankandblank R subscript 3 end subscript are the radii of the circumcircles of triangles O B C comma blank O C A blankandblank O A B comma respectively, then fraction numerator a over denominator R subscript 1 end subscript end fraction plus fraction numerator b over denominator R subscript 2 end subscript end fraction plus fraction numerator c over denominator R subscript 3 end subscript end fraction has the value equal to

  1. fraction numerator a b c over denominator 2 R to the power of 3 end exponent end fraction  
  2. fraction numerator R to the power of 3 end exponent over denominator a b c end fraction  
  3. fraction numerator 4 increment over denominator R to the power of 2 end exponent end fraction  
  4. fraction numerator increment over denominator 4 R to the power of 2 end exponent end fraction  

The correct answer is: fraction numerator a b c over denominator 2 R to the power of 3 end exponent end fraction


    R equals fraction numerator a b c over denominator 4 increment end fraction rightwards double arrow fraction numerator a over denominator R end fraction equals fraction numerator 4 increment over denominator b c end fraction
    rightwards double arrow fraction numerator a over denominator R subscript 1 end subscript end fraction plus fraction numerator b over denominator R subscript 2 end subscript end fraction plus fraction numerator c over denominator R subscript 3 end subscript end fraction equals fraction numerator 4 over denominator R to the power of 2 end exponent end fraction open parentheses increment subscript 1 end subscript plus increment subscript 2 end subscript plus increment subscript 3 end subscript close parentheses equals fraction numerator 4 increment over denominator R to the power of 2 end exponent end fraction

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