Assertion (A): In triangle ABC,if r=6, r_2=36 | vedclass

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(A) For Reason $(R)$: Given $r:R:r_2 = 1:2.5:6 = 2:5:12$.Let $r=2k, R=5k, r_2=12k$.Using the formula $r_2-r = 4R \sin^2 \frac{B}{2}$,we have $12k-2k =

Vedclass · Accepted Answer

Both $(A)$ and $(R)$ are true. $(R)$ is a correct explanation of $(A)$

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(A) For Reason $(R)$: Given $r:R:r_2 = 1:2.5:6 = 2:5:12$.Let $r=2k, R=5k, r_2=12k$.Using the formula $r_2-r = 4R \sin^2 \frac{B}{2}$,we have $12k-2k = 4(5k) \sin^2 \frac{B}{2}$.$10k = 20k \sin^2 \frac{B}{2}$ $\Rightarrow \sin^2 \frac{B}{2} = \frac{1}{2}$ $\Rightarrow \frac{B}{2} = 45^{\circ}$ $\Rightarrow B = 90^{\circ}$.Thus,Reason $(R)$ is true.For Assertion $(A)$: Given $r=6, r_2=36, R=15$.Using $r_2-r = 4R \sin^2 \frac{B}{2}$,we have $36-6 = 4(15) \sin^2 \frac{B}{2}$.$30 = 60 \sin^2 \frac{B}{2}$ $\Rightarrow \sin^2 \frac{B}{2} = \frac{1}{2}$ $\Rightarrow B = 90^{\circ}$.If $B=90^{\circ}$,then $b^2 = a^2+c^2$. Thus,Assertion $(A)$ is true.Since $(R)$ provides the logical basis for the property used in $(A)$,$(R)$ is the correct explanation of $(A)$.

Assertion $(A)$: In $\triangle ABC$,if $r=6, r_2=36, R=15$,then $c^2+a^2=b^2$.
Reason $(R)$: In $\triangle ABC$,if $r:R:r_2=1:2.5:6$,then $B=90^{\circ}$.
The correct option among the following is:

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Assertion $(A)$: In $\triangle ABC$,if $r=6, r_2=36, R=15$,then $c^2+a^2=b^2$.Reason $(R)$: In $\triangle ABC$,if $r:R:r_2=1:2.5:6$,then $B=90^{\circ}$.The correct option among the following is: