In triangle ABC,if r_1 = 2r_2 = 3r_3,then | vedclass

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

Question

(C) Given,in $	riangle ABC$,$r_1 = 2r_2 = 3r_3$. Using the formula $r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,and $r_3 = \frac{\Delta}{s-c

Vedclass · Accepted Answer

$a+c=2b$

Vedclass · Answer

(C) Given,in $	riangle ABC$,$r_1 = 2r_2 = 3r_3$. Using the formula $r_1 = \frac{\Delta}{s-a}$,$r_2 = \frac{\Delta}{s-b}$,and $r_3 = \frac{\Delta}{s-c}$,we have: $\frac{\Delta}{s-a} = 2 \frac{\Delta}{s-b} = 3 \frac{\Delta}{s-c} = k$ (let). Then,$s-a = \frac{1}{k}$,$s-b = \frac{2}{k}$,and $s-c = \frac{3}{k}$. Adding these equations: $(s-a) + (s-c) = \frac{1}{k} + \frac{3}{k} = \frac{4}{k}$. Since $s-b = \frac{2}{k}$,we have $\frac{4}{k} = 2(s-b)$. Thus,$2s - a - c = 2s - 2b$,which simplifies to $a+c = 2b$.

In $\triangle ABC$,if $r_1 = 2r_2 = 3r_3$,then

Similar Questions

In a triangle $ABC$ with usual notations,if $a:b:c = 7:8:9$,then $\cos A : \cos B : \cos C =$

In $\Delta ABC,$ if $(a + b + c)(a - b + c) = 3ac,$ then

If two angles of $\triangle ABC$ are $\frac{\pi}{4}$ and $\frac{\pi}{3}$,then the ratio of the smallest and greatest side is

In a triangle $ABC$,$\frac{a}{b}=2+\sqrt{3}$ and $\angle C=60^{\circ}$. Then the measure of $\angle A$ is (in $^{\circ}$)

In $\triangle ABC$, if $\angle C = \frac{\pi}{3}$, then the value of $\cos^2 A + \cos^2 B + \cos A \cos B$ is...

Vedclass Test Series

Exam Paper Generator

Online Exam Module