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In a $Δ A B C$ , if $r_{1}, r_{2}, r_{3}$ are in H.P., then $a, b, c$ are in

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H.P.

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G.P.

A.P.

answer is A.

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Detailed Solution

$\frac{2}{r_{2}} = \frac{1}{r_{1}} + \frac{1}{r_{3}}$

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

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

$∴ 2 b = a + c \Rightarrow a, b, c a r e i n A . P$

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