CAT Geometry Questions & Solutions

A sample of real CAT Geometry past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 189 Geometry questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   The (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (-3, -2), (1, -5) and (9, 1), respectively. If the diagonal SQ intersects the x-axis at (a, 0) , then the value of a is

   • $\dfrac{27}{7}$

   • $\dfrac{10}{3}$

   • $\dfrac{13}{4}$

   • $\dfrac{29}{9}$

2. Q2.CAT 2024

   A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is

   • $72(2 + \sqrt{2})$

   • $36(1 + \sqrt{2})$

   • $72(1 + \sqrt{2})$

   • $36(2 + \sqrt{2})$

3. Q3.CAT 2022

   Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm., then, the area of the triangle EOD, in sq. cm., is

   Answer: 9

4. Q4.CAT 2020

   The points (2,1) and (-3,-4) are opposite vertices of a parallelogram.If the other two vertices lie on the line $x+9y+c=0$, then c is

   • 12

   • 13

   • 15

   • 14

5. Q5.CAT 2019

   If the rectangular faces of a brick have their diagonals in the ratio $3 : 2 \surd3 : \surd{15}$, then the ratio of the length of the shortest edge of the brick to that of its longest edge is

   • $\sqrt{3} : 2$

   • $1 : \sqrt{3}$

   • $2 : \sqrt{5}$

   • $\sqrt{2} : \sqrt{3}$

6. Q6.CAT 2017

   The area of the closed region bounded by the equation

   I x I + I y I = 2 in the two-dimensional plane is

   • $4\pi$ sq. units

   • 4 sq. units

   • 8 sq. units

   • $2\pi$ sq. units

7. Q7.CAT 2008

   Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq. cm.) of the intersecting region?

   • $\frac{\pi}{3}-\frac{\sqrt 3}{4}$

   • $\frac{2\pi}{3}+\frac{\sqrt 3}{2}$

   • $\frac{4\pi}{3}-\frac{\sqrt 3}{2}$

   • $\frac{4\pi}{3}+\frac{\sqrt 3}{2}$

   • $\frac{2\pi}{3}-\frac{\sqrt 3}{2}$

8. Q8.CAT 2005

   P, Q, S, and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?

   • $2r(1+ \sqrt3)$

   • $2r(2+ \sqrt3)$

   • $r(1+ \sqrt5)$

   • $2r+ \sqrt3$

9. Q9.CAT 2003

   In the triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, the AP:QC is equal to

   • 1:1

   • 3:2

   • 4:1

   • 3:8

10. Q10.CAT 2001

    A square, whose side is 2 m, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres, is

    • $\frac{\sqrt 2}{\sqrt 2 +1}$

    • $\frac{2}{\sqrt 2 + 1}$

    • $\frac{2}{\sqrt 2 - 1}$

    • $\frac{\sqrt 2}{\sqrt 2-1}$

11. Q11.CAT 1999

    Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

    • 495

    • 550

    • 1045

    • 2475

12. Q12.CAT 1997

    In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of CBE to that of ADE?

    • 1 : 4

    • 1 : 2

    • 1 : 3

    • Data insufficient

CAT Geometry previous year questions with solutions — AthenaPrep