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Q.

If $I_{1}$ is the centre of the first described circle , then the value of $\frac{A I_{1}}{r_{1}} =$

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a

$\sec \frac{A}{2}$

b

$cosec \frac{A}{2}$

c

$\sin \frac{A}{2}$

d

$\cos \frac{A}{2}$

answer is B.

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Detailed Solution

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From $Δ A D I_{1},$

$\sin \frac{A}{2} = \frac{r_{1}}{A I_{1}}$

$\Rightarrow A I_{1} = r_{1} cosec \frac{A}{2}$

$\Rightarrow \frac{A I_{1}}{r_{1}} = cossec \frac{A}{2}$

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If I1 is the centre of the first described circle , then the value of AI1r1=