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 $I, II$
- BOnly $II, III$
- COnly $I, III$
- D$I, II, III$
Explore More
Similar Questions
In $\triangle ABC$,suppose the radius of the excircle opposite to angle $A$ is denoted by $r_1$,similarly $r_2$ for angle $B$,and $r_3$ for angle $C$. If $r_1=2, r_2=3, r_3=6$,then what is $(a, b, c)$?
In $\triangle ABC$, if $a : b : c = 4 : 5 : 6$, then the ratio of the circumradius to its inradius is
In a triangle $ABC$,$a : b : c = 4 : 5 : 6$. The ratio of the radius of the circumcircle to that of the incircle is
In a triangle $ABC,$ $a:b:c = 4:5:6$. The ratio of the radius of the circumcircle to that of the incircle is
MediumIIT 1996
View SolutionIf in a $\triangle ABC$, $AD$, $BE$, and $CF$ are the altitudes and $R$ is the circumradius of $\triangle ABC$, then the radius of the circumcircle of $\triangle DEF$ is
MediumWBJEE 2016
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