In triangle ABC,suppose the exradii opposite | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For $	riangle ABC$,the exradii are given by $r_1=\frac{\Delta}{s-a}, r_2=\frac{\Delta}{s-b}, r_3=\frac{\Delta}{s-c}$ and the inradius is $r=\frac

Vedclass · Accepted Answer

$4R$

Vedclass · Answer

(A) For $	riangle ABC$,the exradii are given by $r_1=\frac{\Delta}{s-a}, r_2=\frac{\Delta}{s-b}, r_3=\frac{\Delta}{s-c}$ and the inradius is $r=\frac{\Delta}{s}$,where $\Delta$ is the area of the triangle and $s$ is the semi-perimeter.We know the identity $r_1+r_2+r_3 = 4R+r$.Rearranging this,we get $r_1+r_2+r_3-r = 4R$.Given $r_1=2, r_2=3, r_3=6$,we can find $r$ using the relation $\frac{1}{r} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}$.$\frac{1}{r} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = \frac{3+2+1}{6} = 1$.Thus,$r=1$.Substituting the values,$r_1+r_2+r_3-r = 2+3+6-1 = 10$.Since $r_1+r_2+r_3-r = 4R$,we have $10 = 4R$,so $R = 2.5$.The expression $r_1+r_2+r_3-r$ is equal to $4R$.

In $\triangle ABC$,suppose the exradii opposite to angles $A, B$ and $C$ are denoted by $r_1, r_2$ and $r_3$ respectively. If $r_1=2, r_2=3, r_3=6$ and $R$ is the radius of the circumcircle,then the value of $r_1+r_2+r_3-r$ is:

Similar Questions

In a triangle $ABC,$ $a:b:c = 4:5:6$. The ratio of the radius of the circumcircle to that of the incircle is

If $a, b, c$ are the sides of a $\Delta ABC$ and exradii $r_1, r_2, r_3$ are respectively $12, 6, 4$, then $a+2b+3c=$

If $a, b$ and $c$ are the sides of $\triangle ABC$ for which $r_1=8, r_2=12$ and $r_3=24$,then the ordered triad $(a, b, c)=$

$ABC$ is an isosceles triangle with an inscribed circle with center $O$. Let $P$ be the midpoint of $BC$. If $AB = AC = 15$ and $BC = 10$, then $OP$ equals

In $\triangle ABC$,if $a=8, b=10, c=12$,then $\frac{r}{R}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module