Properties of Triangles — JEE Main PYQs & Practice Questions

Properties of Triangles is a Mathematics chapter in the JEE Main syllabus. This page brings together 11 previous-year and practice questions on Properties of Triangles, organised into 3 topics: Sine and Cosine Rule, Area of Triangle and Inradius and Circumradius. Most questions come with a step-by-step solution you can work through free in PrepWiser.

Chapter weightage: how many questions each chapter had per shift in the 2024–26 papers.

Sine and Cosine Rule

• In a triangle ABC,BC=7,AC=8,AB=α∈ N and cos A=2/3. If 49 cos (3C)+42=m/n, where gcd…
• In any triangle ABC, a/sin A = b/sin B = c/sin C is:
• In a triangle, if sides are 3, 4, 5, then it is a x triangle (right/acute/obtuse).
• Consider a triangle ABC having the vertices A(1,2),B(α,β) and C(γ,δ) and angles ∠…

Area of Triangle

• Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively…
• Let a triangle ABC be inscribed in the circle x² - √2 (x + y) + y² = 0 such that ∠ BAC =…

Inradius and Circumradius

• In any triangle, sum of any two sides is greater than the third side.
• Two vertices of a triangle ABC are A(3,-1) and B(-2,3), and its orthocentre is P(1,1)…
• Let the area of a △ PQR with vertices P(5,4),Q(-2,4) and R(a,b) be 35 square units. If…
• A circle is inscribed in an equilateral triangle of side of length 12. If the area and…
• Let A(6,8),B(10 cos α,-10 sin α) and C(-10 sin α,10 cos α), be the vertices of a…

More Mathematics chapters

• Sets
• Relations & Functions (Basic)
• Trigonometric Ratios & Identities
• Trigonometric Equations
• Inverse Trigonometric Functions
• Complex Numbers
• Quadratic Equations & Polynomial Inequalities
• Sequences & Series
• Binomial Theorem
• Permutations & Combinations
• Mathematical Induction
• Statistics
• Probability — Basic
• Straight Lines
• Circles
• Parabola
• Ellipse
• Hyperbola
• Limits
• Continuity & Differentiability
• Differentiation
• Applications of Derivatives
• Indefinite Integration
• Definite Integration
• Area Under Curves
• Differential Equations
• Vectors
• Three Dimensional Geometry
• Matrices
• Determinants
• Functions (Advanced)
• Probability — Advanced

Frequently asked questions

How many Properties of Triangles questions are there for JEE Main?

PrepWiser has 11 Properties of Triangles questions for JEE Main, grouped into 3 topics such as Sine and Cosine Rule, Area of Triangle and Inradius and Circumradius.

Are these Properties of Triangles questions from previous-year JEE Main papers?

Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.

Where can I see the answers and solutions to these Properties of Triangles questions?

Open any Properties of Triangles question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.