In a $△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} =$

s

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{(\frac{Δ}{r})}^{2}

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\frac{Δ}{s}

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Δ^{2}

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Solution

The correct option is B ${(\frac{Δ}{r})}^{2}$
We know $r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{Δ^{2}}{(s - a) (s - b)} + \frac{Δ^{2}}{(s - b) (s - c)} + \frac{Δ^{2}}{(s - c) (s - a)}$

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

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A B C

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r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = ?

A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} =

r_{1} (r_{2} + r_{3}) / a = r_{2} (r_{3} + r_{1}) / b = r_{3} (r_{1} + r_{2}) / c

a (r r_{1} + r_{2} r_{3}) = b (r r_{2} + r_{3} r_{1}) = c (r r_{3} + r_{1} r_{2}) = a b c

\frac{r_{1} (r_{2} + r_{3})}{\sqrt{r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1}}} =

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