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NDA Properties of Triangles questions with solutions

Sine rule, cosine rule and triangle centres. 18 questions from our 2016–2025 NDA pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

NDA 2025

A triangle: 1. For a triangle with sides 5,12,13, the circumradius is 6.5. 2. In every triangle the circumcentre lies inside the triangle.NDA 2025 Maths · medium
Its circumradius isNDA 2025 Maths · medium

NDA 2024

A triangle ABC is/are correct? 1. If no angle is a right angle, tan A+tan B+tan C=tan Atan Btan C. 2. The sum of any two sides is less than the third…NDA 2024 Maths · easy

NDA 2023

In a triangle ABC, the angles satisfy A:B:C=1:2:3. The ratio of the sides a:b:c isNDA 2023 Maths · medium
The cosine of its largest angle isNDA 2023 Maths · medium
The radius of its incircle isNDA 2023 Maths · medium
For a triangle ABC with usual notation: 1. a=bcos C+ccos B. 2. If a^2+b^2<c^2, then the angle C is obtuse.NDA 2023 Maths · medium

NDA 2022

The inradius of a triangle with sides 13,14,15 isNDA 2022 Maths · medium

NDA 2020

For a triangle ABC, consider the following statements: 1. tan A+tan B+tan C=tan Atan Btan C holds for every triangle. 2. cos A+cos B+cos C≤3/2.NDA 2020 Maths · medium

NDA 2019

The inradius of a triangle with sides 9, 40 and 41 isNDA 2019 Maths · easy
The area of a triangle with two sides 6 and 8 and the included angle 150^° isNDA 2019 Maths · easy
In a triangle ABC which is not right-angled, tan A+tan B+tan C=tan Atan Btan C. 2. In any triangle ABC, sin (A+B)=-sin C.NDA 2019 Maths · medium

NDA 2017

The angle B isNDA 2017 Maths · easy
For a triangle with sides a,b,c, consider the statements. 1. If a^2+b^2<c^2, then angle C is obtuse. 2. If a:b:c=1:√3:2, then the triangle is…NDA 2017 Maths · medium

NDA 2016

In a triangle ABC, A=45^°, B=60^° and a=√6. The length of side b isNDA 2016 Maths · easy
In a triangle ABC with the usual notation, bcos C+ccos B is equal toNDA 2016 Maths · easy
The area of a triangle whose sides are 4, 5 and 6 isNDA 2016 Maths · medium
In a triangle ABC, cot Acot B=2 and cot Bcot C=3. Then cot Ccot A is equal toNDA 2016 Maths · hard