In ΔABC if r1+sr1=2 then b2+c2−a22bc=

r1+sr1=21+sr1=21+sstanA2=21+cotA2=2cotA2=2−1cotA2=cot67120A=1350b2+c2−a22bc=cosA=cos1350=−12

In ΔABC if r1+sr1=2 then b2+c2−a22bc=

r1+sr1=21+sr1=21+sstanA2=21+cotA2=2cotA2=2−1cotA2=cot67120A=1350b2+c2−a22bc=cosA=cos1350=−12

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In $Δ A B C$ if $\frac{r_{1} + s}{r_{1}} = \sqrt{2}$ then $\frac{b^{2} + c^{2} - a^{2}}{2 b c} =$

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$\frac{1}{\sqrt{2}}$

$- \frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$

$- \frac{\sqrt{3}}{2}$

answer is B.

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Detailed Solution

$\frac{r_{1} + s}{r_{1}} = \sqrt{2}$

$1 + \frac{s}{r_{1}} = \sqrt{2}$

$1 + \frac{s}{s \tan \frac{A}{2}} = \sqrt{2}$

$1 + \cot \frac{A}{2} = \sqrt{2}$

$\cot \frac{A}{2} = \sqrt{2} - 1$

$\cot \frac{A}{2} = \cot 67 {\frac{1}{2}}^{0}$

$A = 135^{0}$

$\frac{b^{2} + c^{2} - a^{2}}{2 b c} = \cos A = \cos 135^{0} = \frac{- 1}{\sqrt{2}}$

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In $Δ A B C$ if $\frac{r_{1} + s}{r_{1}} = \sqrt{2}$ then $\frac{b^{2} + c^{2} - a^{2}}{2 b c} =$