MHT CET · Maths · Properties of Triangles
In \(\triangle A B C\), if \(\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos c}{c}\) with usual notations, then the triangle is
- A an isosceles triangle
- B an equilateral triangle
- C a right angled scalene triangle
- D a scalene triangle
Answer & Solution
Correct Answer
(B) an equilateral triangle
Step-by-step Solution
Detailed explanation
From sine rule \(a / \sin A=b / \sin B=c / \sin C=2 R\)
Given situation
\(a / \cos A=b / \cos B=c / \cos B=k\)
\(2 R \sin A=k \cos A\)
\(\tan A=\tan B=\tan C\)
Hence it is equilateral triangle.
Given situation
\(a / \cos A=b / \cos B=c / \cos B=k\)
\(2 R \sin A=k \cos A\)
\(\tan A=\tan B=\tan C\)
Hence it is equilateral triangle.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If surrounding air is kept at \(20^{\circ} \mathrm{C}\) and body cools from \(80^{\circ} \mathrm{C}\) to \(70^{\circ} \mathrm{C}\) in 5 minutes, then the temperature of the body after 15 minute will beMHT CET 2022 Hard
- If \(\int \mathrm{f}(x) \mathrm{d} x=\psi(x)\), then \(\int x^5 \mathrm{f}\left(x^3\right) \mathrm{d} x\) is equal toMHT CET 2024 Easy
- The area bounded by the parabola \(y=x^2\) and the line \(y=x\) isMHT CET 2021 Hard
- A plane meets the axes in \(A, B\) and \(C\) such that centroid of the \(\Delta A B C\) is \((1,2,3)\). The equation of the plane isMHT CET 2011 Hard
- \(\int_{0}^{\frac{\pi}{2}} \frac{1-\cot x}{\operatorname{cosec} x+\cos x} d x=\)MHT CET 2020 Easy
- and are two points with position vectors and respectively. The position vector of the point which divides the line segment in the ratio externally isMHT CET 2018 Medium
More PYQs from MHT CET
- A ray of light is incident on one face of an equilateral glass prism having refractive index \(\sqrt{2}\). It produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence isMHT CET 2021 Hard
- A door 1.2 mwide requires a force of \(1 \mathrm{~N}\) to be applied perpendicular at the free end to open or close it. The perpendicular force required at a point 0.2 mdistant from the hinges for opening or closing the door isMHT CET 2022 Easy
- Identify product ' \(B\) ' in following reaction
\(\text {Benzonitrile } \xrightarrow[\text { Dry ether }]{\mathrm{C}_6 \mathrm{H}_5 \mathrm{Mgr}} \mathrm{~A} \xrightarrow{\mathrm{H}_3 \mathrm{O}^{+}}\)
MHT CET 2024 Easy - A satellite moves in a stable circular orbit round the earth if (where \(\mathrm{V}_{\mathrm{H}}, \mathrm{V}_{\mathrm{c}}\) and \(\mathrm{V}_{\mathrm{e}}\) are the horizontal velocity, critical velocity and escape velocity respectively)MHT CET 2023 Easy
- Which of the following polymer is used in paints?MHT CET 2019 Easy
- If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at \(47^{\circ} \mathrm{C}\), the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)MHT CET 2025 Medium