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In $Δ A B C, (r_{1} - r) (r_{2} - r) (r_{3} - r) =$

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$4 R s^{2}$

$4 R r^{2}$

answer is B.

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Detailed Solution

$(\frac{Δ}{s - a} - \frac{Δ}{s}) (\frac{Δ}{s - b} - \frac{Δ}{s}) (\frac{Δ}{s - c} - \frac{Δ}{s})$

$= Δ^{3} [\frac{s - s + a}{s (s - a)} . \frac{s - s + b}{s (s - b)} . \frac{s - s + c}{s (s - c)}]$

$\begin{array}{l} = Δ^{3} . \frac{a b c}{Δ^{2}} \times \frac{1}{s^{2}} = Δ^{3} \frac{4 R Δ}{Δ^{2}} \times \frac{1}{s^{2}} \\ = 4 R {(\frac{Δ}{s})}^{2} = 4 R r^{2} \end{array}$

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