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Construction of Incircle

In ABC, R =...

Question

In $△ A B C, R = 10,$ then the value of $\frac{r (a + b + c)}{a b c}$ is

A

\frac{1}{40}

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B

\frac{1}{50}

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C

\frac{1}{10}

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D

\frac{1}{20}

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Solution

The correct option is D $\frac{1}{20}$
$\frac{r (a + b + c)}{a b c} = \frac{Δ}{s} \cdot 2 s \cdot \frac{1}{a b c}$

$= \frac{2 Δ}{a b c} = \frac{1}{2 R} = \frac{1}{20}$

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