Maths-
General
Easy

Question

Assertion : In a triangle ABC; the harmonic mean of the exradii is 3 times the inradius.
Reason : In any triangle ABC; r1 + r2 + r3 = 4R.

  1. If both (A) and (R) are true, and (R) is the correct explanation of (A).  
  2. If both (A) and (R) are true but (R) is not the correct explanation of (A).  
  3. If (A) is true but (R) is false.  
  4. If (A) is false but (R) is true.  

The correct answer is: If (A) is true but (R) is false.


    Assertion : Harmonic mean of exradii
    = fraction numerator 3 over denominator fraction numerator 1 over denominator r subscript 1 end subscript end fraction plus fraction numerator 1 over denominator r subscript 2 end subscript end fraction plus fraction numerator 1 over denominator r subscript 3 end subscript end fraction end fraction = fraction numerator 3 over denominator fraction numerator s minus a over denominator capital delta end fraction plus fraction numerator s minus b over denominator capital delta end fraction plus fraction numerator s minus c over denominator capital delta end fraction end fraction =fraction numerator 3 capital delta over denominator s end fraction= 3r
     Assertion is true.
    Reason : r1 + r2 + r3 = 4R
    fraction numerator capital delta over denominator s minus a end fraction plus fraction numerator capital delta over denominator s minus b end fraction plus fraction numerator capital delta over denominator s minus c end fraction = 4R fraction numerator a b c over denominator 4 R end fraction = 
    fraction numerator 1 over denominator s minus a end fraction plus fraction numerator 1 over denominator s minus b end fraction plus fraction numerator 1 over denominator s minus c end fraction= fraction numerator 4 R over denominator capital delta end fraction equals fraction numerator a b c over denominator capital delta to the power of 2 end exponent end fraction
     Reason is false.

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