In a $\triangle ABC$,which of the following formulae are correct?
$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
$II. r_1 = (s-a) \tan \frac{A}{2}$
$III. r_3 = \frac{\Delta}{s-c}$
$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
$II. r_1 = (s-a) \tan \frac{A}{2}$
$III. r_3 = \frac{\Delta}{s-c}$
- AOnly $I$ and $II$
- BOnly $II$ and $III$
- COnly $I$ and $III$
- D$I, II,$ and $III$
Explore More
Similar Questions
Let $A$ be the area of the in-circle and $A_1, A_2, A_3$ be the areas of the ex-circles of a triangle. If $A_1=4, A_2=9, A_3=16$, then $A=$
If $r$ is the inradius,$\Delta$ is the area of $\triangle ABC$,and $s$ is the semi-perimeter,then which of the following is true?
In a $\triangle ABC$,let $a, b, c, s, r, R, I, S, r_1, r_2, r_3$ stand for their usual meanings. Match the items of List-$I$ with those of List-$II$.
List-$I$ List-$II$ $A. \tan \frac{A}{2} = \frac{r}{s-a}$ $I. (AI) \left( \frac{\sqrt{(s-b)(s-c)}}{bc} \right)$ $B. r$ $II. R^2$ $C. (SI)^2 + 2Rr$ $III. (4R + r + \sqrt{2}s)(4R + r - \sqrt{2}s)$ $D. r_1^2 + r_2^2 + r_3^2$ $IV. \frac{Rr}{S}$ $V. \frac{(s-b)(s-c)}{\Delta}$
The correct match is:
| List-$I$ | List-$II$ |
| $A. \tan \frac{A}{2} = \frac{r}{s-a}$ | $I. (AI) \left( \frac{\sqrt{(s-b)(s-c)}}{bc} \right)$ |
| $B. r$ | $II. R^2$ |
| $C. (SI)^2 + 2Rr$ | $III. (4R + r + \sqrt{2}s)(4R + r - \sqrt{2}s)$ |
| $D. r_1^2 + r_2^2 + r_3^2$ | $IV. \frac{Rr}{S}$ |
| $V. \frac{(s-b)(s-c)}{\Delta}$ |
The correct match is:
If the lengths of the sides of a triangle are $3, 4$ and $5$ units,then $R$ (the circumradius) is ............ $unit$.
Medium
View SolutionIf $R$ is the radius of the circumcircle of the $\Delta ABC$ and $\Delta$ is its area,then
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo