(C) Statement $I$: We know that $r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$. This is a standard identity in a triangle. Thus,$I$ is tr

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(C) Statement $I$: We know that $r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$. This is a standard identity in a triangle. Thus,$I$ is true.Statement $II$: We know that $r_1 = s \tan \frac{A}{2}$. The given formula $r_1 = (s-a) \tan \frac{A}{2}$ is incorrect. Thus,$II$ is false.Statement $III$: We know that $r_3 = \frac{\Delta}{s-c}$. This is a standard formula for the exradius $r_3$. Thus,$III$ is true.Therefore,statements $I$ and $III$ are correct.

Class 11 Mathematics Trigonometrical Equations Circle connected with triangle

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In a $\triangle ABC$,which of the following formulae are correct?
$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
$II. r_1 = (s-a) \tan \frac{A}{2}$
$III. r_3 = \frac{\Delta}{s-c}$

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A
Only $I, II$
B
Only $II, III$
C
Only $I, III$
D
$I, II, III$

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Circle connected with triangle

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In a $\triangle ABC$,which of the following formulae are correct?$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$$II. r_1 = (s-a) \tan \frac{A}{2}$$III. r_3 = \frac{\Delta}{s-c}$

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In a $\triangle ABC$,which of the following formulae are correct?
$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
$II. r_1 = (s-a) \tan \frac{A}{2}$
$III. r_3 = \frac{\Delta}{s-c}$