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Question

# STATEMENT 1: In a ΔABC, if r1, r2, r3 are in H.P. then r2r=13STATEMENT 2: In a ΔABC,1r1+1r2+1r3=2r

A
Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation of Statement- 1
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B
Statement-1 is true, Statement-2 is true, Statement-2 is not correct explanation for Statement-1
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C
Statement-1 is true, Statement-2 is false
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D
Statement-1 is false, Statement-2 is false
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Solution

## The correct option is D Statement-1 is false, Statement-2 is falseIf r1,r2,r3 are in G.P then 2r2=1r1+1r32(s−b)Δ=(s−a)Δ+(s−c)Δ2s−2b=s−a+s−ca+c=2b......(i) r2r=Δs−bΔs=ss−b Substituting (i) r2r=a+c+ba+c−br2r=2b+b2b−b=3 So statement (i) is false 1r1+1r2+1r3=s−aΔ+s−bΔ+s−cΔ=3s−a−b−cΔ=sΔ So statement 2 is also false

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