If the radius of the incircle of a triangle w | vedclass

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

Question

(B) Let the sides of the triangle be $a = 5k, b = 5k, c = 6k$. First, we find the value of $k$ using the inradius formula $r = \frac{\Delta}{s}$. The

Vedclass · Accepted Answer

$	an^{-1}\left(\frac{24}{7}ight)$

Vedclass · Answer

(B) Let the sides of the triangle be $a = 5k, b = 5k, c = 6k$. First, we find the value of $k$ using the inradius formula $r = \frac{\Delta}{s}$. The semi-perimeter $s = \frac{5k + 5k + 6k}{2} = 8k$. The area $\Delta = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{8k(3k)(3k)(2k)} = \sqrt{144k^4} = 12k^2$. Given $r = 6$, so $6 = \frac{12k^2}{8k}$ $\Rightarrow 6 = \frac{3k}{2}$ $\Rightarrow k = 4$. The sides are $20, 20, 24$. In the isosceles triangle, the altitude to the base $6k$ divides it into two triangles with base $3k$ and hypotenuse $5k$. The height is $\sqrt{(5k)^2 - (3k)^2} = 4k$. Let the vertex angle be $2	heta$. Then $	an 	heta = \frac{3k}{4k} = \frac{3}{4}$. The vertex angle is $2	heta$, where $	an 2	heta = \frac{2 	an 	heta}{1 - 	an^2 	heta} = \frac{2(3/4)}{1 - (9/16)} = \frac{3/2}{7/16} = \frac{24}{7}$. Thus, the largest angle is $	an^{-1}\left(\frac{24}{7}ight)$.

If the radius of the incircle of a triangle with sides $5k, 6k$ and $5k$ is $6$, then the largest angle of that triangle is

Similar Questions

Let $S=\{x \in(-\pi, \pi) \mid x \neq 0, \pm \frac{\pi}{2}\}$. The sum of all distinct solutions of the equation $\sqrt{3} \sec x+\operatorname{cosec} x+2(\tan x-\cot x)=0$ in the set $S$ is equal to

With usual notations, in $\triangle ABC$, if $2a^2 = b^2 + c^2$, then $\frac{\cos 3A}{\cos A} + 2 = $

If $A, B, C$ are the angles of a triangle,then $\sum \frac{\cot A + \cot B}{\tan A + \tan B} = $

In $\triangle ABC$,if $a, b$ and $c$ are in arithmetic progression,then $\cos A + 2 \cos B + \cos C =$

If angles $A$,$B$,and $C$ of a $\Delta ABC$ are $75^o$,$45^o$,and $60^o$ respectively,then the ratio of the areas of $\Delta OBC$,$\Delta COA$,and $\Delta AOB$ respectively is [where $O$ is the circumcentre of the triangle].

Vedclass Test Series

Exam Paper Generator

Online Exam Module