(A) We know that in a triangle,the area $\Delta = rs = \frac{abc}{4R}$.Also,the expression $\frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca}$ can be written

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

(A) We know that in a triangle,the area $\Delta = rs = \frac{abc}{4R}$.Also,the expression $\frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca}$ can be written as $\frac{a+b+c}{abc} = \frac{2s}{abc}$.From the area formula,$abc = 4R\Delta = 4R(rs) = 4Rrs$.Substituting this into the expression,we get $\frac{2s}{4Rrs} = \frac{1}{2Rr}$.Given $r=3$ and $R=5$,the value is $\frac{1}{2 \times 5 \times 3} = \frac{1}{30}$.

Class 11 Mathematics Trigonometrical Equations Relation between sides and angles, Solutions of triangles

Medium

In $\triangle ABC$,if $r=3$ and $R=5$,then $\frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = $

AP EAMCET 2025 All AP EAMCET

A
$\frac{1}{30}$
B
$\frac{12}{15}$
C
$\frac{1}{15}$
D
$\frac{5}{36}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Equations

Subtopic

Relation between sides and angles, Solutions of triangles

Previous Year

AP EAMCET 2025 Paper All AP EAMCET years →

In $\Delta ABC$,if $a = 2$,$b = 4$,and $\angle C = 60^\circ$,then $\angle A$ and $\angle B$ are equal to:

Medium

View Solution

If $\cot \left(\frac{A}{2}\right)=\sqrt{\frac{1+a}{1-a}} \cdot \cot \left(\frac{\theta}{2}\right)$,then $\cos \theta=$

EasyTS EAMCET 2020

View Solution

In a $\triangle ABC$,$(a-b)^2 \cos^2 \frac{C}{2} + (a+b)^2 \sin^2 \frac{C}{2}$ is equal to

MediumTS EAMCET 2004

View Solution

In $\triangle ABC$,$\angle B = \frac{\pi}{4}$ and $\angle C = \frac{\pi}{3}$. If the area of the triangle is $54 + 18\sqrt{3}$ sq. units,then $a =$

MediumTS EAMCET 2021

View Solution

In $\Delta ABC$,$\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} = $

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In $\triangle ABC$,if $r=3$ and $R=5$,then $\frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = $

Similar Questions

In $\Delta ABC$,if $a = 2$,$b = 4$,and $\angle C = 60^\circ$,then $\angle A$ and $\angle B$ are equal to:

If $\cot \left(\frac{A}{2}\right)=\sqrt{\frac{1+a}{1-a}} \cdot \cot \left(\frac{\theta}{2}\right)$,then $\cos \theta=$

In a $\triangle ABC$,$(a-b)^2 \cos^2 \frac{C}{2} + (a+b)^2 \sin^2 \frac{C}{2}$ is equal to

In $\triangle ABC$,$\angle B = \frac{\pi}{4}$ and $\angle C = \frac{\pi}{3}$. If the area of the triangle is $54 + 18\sqrt{3}$ sq. units,then $a =$

In $\Delta ABC$,$\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module