CAT Triangles questions with solutions
Properties of triangles, similarity and related circles. 24 questions from our 2016–2025 CAT pattern papers. Each has the answer and a full solution.
CAT 2025
CAT 2022
CAT 2021
- In a right-angled triangle, the two sides containing the right angle measure 15 cm and 20 cm. What is the sum of its inradius and circumradius?
- In triangle ABC, AB = 13, BC = 14 and CA = 15. What is the distance between the incentre and the circumcentre of the triangle?
- The two perpendicular sides of a right-angled triangle measure 20 cm and 21 cm.
CAT 2020
CAT 2019
- The two shorter sides of a right-angled triangle are 20 cm and 21 cm. What is the radius of the circle inscribed in the triangle?
- The line segment AE intersects the diagonal BD at F. What is the area of triangle BEF (in cm²)?
- A right-angled triangle has legs of length 20 cm and 21 cm.
- E is the midpoint of BC. The line segment AE meets the diagonal BD at F. What is the area of triangle BEF?
CAT 2018
- The sides of a triangle are 13 cm, 14 cm and 15 cm.
- In triangle ABC, AB = AC = 10 cm and BC = 12 cm. Find the radius (in cm) of the circle passing through A, B and C.
- A triangle has sides 13 cm, 14 cm and 15 cm. What is the radius (in cm) of its inscribed circle?
- In triangle ABC, D is a point on BC with BD : DC = 2 : 3, and E is a point on AD with AE : ED = 3 : 1. What is the ratio of the area of triangle ABE…
CAT 2017
- In a right-angled triangle, the two sides containing the right angle measure 9 cm and 12 cm. What is the length (in cm) of the perpendicular drawn…
- The sides of a triangle are 13 cm, 14 cm and 15 cm. What is the radius (in cm) of the circle that passes through all three vertices of the triangle?
- The segment AE intersects the diagonal BD at point F. What is the area of triangle BEF?
- In triangle ABC, points D and E lie on AB and AC respectively such that DE is parallel to BC and AD : DB = 2 : 3. If the area of the quadrilateral…
CAT 2016
Other Quant topics
Time, Speed and Distance 38Time and Work 23Pipes and Cisterns 11Simple and Compound Interest 33Profit, Loss and Discount 42Mixtures and Alligation 35Ratio and Partnership 17Percentages 30Averages 19Permutations, Combinations and Sets 28Probability 20Logarithms and Indices 16Quadratic Equations and Polynomials 18Linear Equations 9Inequalities and Modulus 19Functions 22Maxima and Minima 11Progressions 29Remainders and Divisibility 15Number System 19Coordinate Geometry 29Circles 18Polygons and Quadrilaterals 12Mensuration 13