With usual notation in a △ABC, if (1r1+1r2)(1r2+1r3)(1r3+1r1)=KR3a2b2c2, then K has the value equal to
A
64.00
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B
64.0
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C
64
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Solution
We know that, r1=△s−a,r2=△s−b,r3=△s−c
Now, (1r1+1r2)(1r2+1r3)(1r3+1r1)=(s−a△+s−b△)(s−b△+s−c△)(s−c△+s−a△)=(2s−(a+b)△)(2s−(b+c)△)(2s−(a+c)△)=c△⋅a△⋅b△=abc△3…(1) ∵R=abc4△⇒△=abc4R
Putting the value of △ in equation (1), abc(abc)3×(4R)3=64R3a2b2c2=KR3a2b2c2 ⇒K=64