Maths-
General
Easy

Question

I f blank x comma y comma z are perpendicular drawn from the vertices of a triangle having a, band c, then fraction numerator b x over denominator c end fraction plus fraction numerator c y over denominator a end fraction plus fraction numerator a z over denominator b end fraction is equal to

  1. fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator 2 R end fraction    
  2. fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator R end fraction    
  3. fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator 4 R end fraction    
  4. fraction numerator 2 open parentheses a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses over denominator R end fraction    

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


    fraction numerator 1 over denominator 2 end fraction a x equals capital delta comma fraction numerator 1 over denominator 2 end fraction b y equals capital delta comma fraction numerator 1 over denominator 2 end fraction C z equals capital delta
    rightwards double arrow x equals fraction numerator 2 capital delta over denominator a end fraction comma y equals fraction numerator 2 capital delta over denominator b end fraction comma z equals fraction numerator 2 capital delta over denominator c end fraction
    fraction numerator b x over denominator c end fraction plus fraction numerator c y over denominator a end fraction plus fraction numerator a z over denominator b end fraction equals fraction numerator 2 b capital delta over denominator a c end fraction plus fraction numerator 2 c capital delta over denominator a b end fraction plus fraction numerator 2 a capital delta over denominator b c end fraction
    fraction numerator 2 capital delta over denominator a b c end fraction open square brackets b to the power of 2 end exponent plus c to the power of 2 end exponent plus a to the power of 2 end exponent close square brackets equals fraction numerator 4 capital delta over denominator a b c end fraction open parentheses fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator 2 end fraction close parentheses
    equals fraction numerator 1 over denominator R end fraction open parentheses fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator 2 end fraction close parentheses
    open parentheses text since  end text R equals fraction numerator a b c over denominator 4 capital delta end fraction close parentheses

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