Question

If $r_1,r_2,r_3$ are in H.P, then the sides are in

• A. G.P
• B. H.P
• C. A.P
• D. none

Answer 1

The correct option is C A.P

Given $r_1,r_2$ & $r_3$ are in H.P

$\frac{1}{r_1}+\frac{1}{r_3}=\frac{2}{r_2}$

$\frac{s-a}{S}+\frac{s-c}{S}=\frac{2(s-b)}{S}$

$\Rightarrow 2s-(a+c)=2(s-b)$

$\Rightarrow b=2(s-b)$

$\Rightarrow b=2s-2b\Rightarrow 2s=3b$

$\Rightarrow a+b+c=3b\Rightarrow a+c=2b$

$\Rightarrow a,b,c$ are in A.P