Geometry Questions For CAT Exam

By Anjali Chowdhury|Updated : March 28th, 2022

Geometry Questions for CAT typically test the candidate’s ability to solve questions based on Circles, Triangles, Polygons, Co-ordinate Geometry, etc. In the CAT Exam, there are 3-4  geometry questions. The geometry questions consist of both topics from Geometry and Mensuration. This is an important topic of the CAT exam. Geometry Questions for CAT are usually solved using various formulas therefore it is important to note all the important concepts, question trends, important formulas, and more.

In CAT 2021, there was a total of 22 questions out of which 3 questions each in Slot 1 and Slot 2 were from Geometry and Mensuration, while Slot 3 consisted of 4 questions on Geometry and Mensuration. The CAT Geometry Questions generally consist of concepts that the candidate must have studied in high school. The difficulty level of Geometry questions of CAT is usually Easy to Moderate. In this article, you will get all the necessary information related to Geometry Questions for CAT.

Table of Content

Outline of Topics Covered in Geometry Questions for CAT

The candidates, aiming at CAT 2022, must the important topics that are needed to be covered to ace Geometry Questions in CAT. Note the below points to get an overview of the topics that must be covered to ace this section.

  • Quadrant System
  • Distance between Two Lines
  • Line Equation and Circle Equation
  • Angles (Supplementary, Complementary, Obtuse, Acute, and Right)
  • Theorems (Pythagoras, Midpoint, Apollonius, Basic Proportionality, Internal and External Angular Bisector, etc.)
  • Cyclic Quadrilateral (Properties and Formulas)
  • Areas and Formulas of Hexagonal Polygon, Triangle, Rectangle. Square, Rhombus, Trapezoid, etc.
  • Special Triangle
  • Circumradius and Inradius
  • Similar and Congruent Triangle
  • Volume, Total Surface Area, and Lateral Surface Area of Different Solid like Cube, Cuboid, Cylinder, Pyramid, Cone, Sphere, Hemisphere, and Frustum

(Note: The candidates must one thing that there is no limitation of Geometry Syllabus for the CAT Exam. So, you need to be prepared for all the related topics to ace Geometry Questions for CAT).

Geometry Questions for CAT Formulas 

The geometry is a part of the quantitative ability section of CAT that consists of several formulas and theorems. The candidates must have a good knowledge of the formulas and theorem to score well and easily solve all Geometry Questions for CAT. Given below are some of the formulas related to geometry: 

Candidates must understand and memorize all the important formulas to solve CAT Geometry Questions quickly and accurately in CAT 2022

General equation of a circle: The general equation of a circle is x2+y2+2gx+2fy+c=0 

  • The Centre of the circle is (-g,-f) 
  • If the origin is the center of the circle then the equation of the circle is x2+y2=r2.

Pythagoras Theorem : In a right angled triangle ABC where ∠B=900 , AC2 = AB2 + BC2

Apollonius Theorem: In a triangle ABC, if AD is the median to side BC then by Apollonius theorem, 2∗(AD2+BD2 ) = AC2 + AB2

For any two similar triangles: Ratio of sides = Ratio of medians = Ratio of heights = Ratio of circumradii = Ratio of Angular bisectors 

The ratio of areas = Ratio of the square of the sides. Tests of similarity : (AA / SSS / SAS) 

Tricks to Solve Geometry Questions for CAT

The CAT geometry is an important part of the quantitative ability section of the CAT exam. Therefore, to score well in this section, the candidates must have good knowledge of the type of Geometry Questions asked in CAT, the formulas for geometry questions for CAT, and also the tricks to solve the Geometry Questions for CAT.

The candidates can follow the below-mentioned tricks to solve Geometry Questions for CAT:

  • The candidates should start with the basic concepts of various topics under Geometry such as lines and angles, polygons, trigonometry, etc.
  • The candidates should have a habit of drawing figures and solving questions this will save time and they will be able to solve the questions faster.
  • The candidates need to have the skill of identifying which formula/concept/method/theorem has to be used only by looking at the question. These skills can be acquired by the candidates only by practice.
  • The candidates should look for questions that require multiple formulas and concepts to be solved.
  • The previous year's CAT question paper needs to be solved by the candidates so that they get an idea about the type of geometry questions asked in CAT.

Best Books for CAT Geometry Questions

Geometry is an important part of the CAT exam therefore the candidates need to prepare well for this topic to score well in the Quantitative Aptitude section of the CAT exam. The candidates must follow the best books for CAT Geometry Questions. Here is the list is given of some popular CAT Books for Geometry Questions in CAT:

Book Name

Author/Publication

Geometry and Higher Mathematics For The CAT and Other MBA exams

Pearson

How to Prepare for Quantitative Aptitude for CAT

Arun Sharma

Quantitative Aptitude-Quantum

Sarvesh Kumar Verma

Geometry for CAT PDF

The candidates need to be comfortable with the types of Geometry questions for the CAT Exam. It is very important and highly recommended to learn shortcut tricks for Geometry for CAT by practicing a lot. Click on the link below to get some questions with solutions so that you could understand the types and difficulty levels of these questions.

Previous Year Geometry Questions for CAT 

Q- In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
(A) 17.05
(B) 27.85
(C) 22.45
(D) 32.25
(E) 26.25

Solution: The correct option is E.
The formula for the circumradius of a triangle

byjusexamprep 

Q-Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD, and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?

(A) geometry questions for CAT
(B)geometry questions for CAT

(C) geometry questions for CAT

(D)geometry questions for CAT
(E)geometry questions for CAT

Solution: The correct option is E.

geometry questions for CAT

geometry questions for CAT

Q-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?

(A)geometry questions for CAT
(B)geometry questions for CAT
(C) geometry questions for CAT
(D)geometry questions for CAT
(E)geometry questions for CAT

Solution: The correct option is E.

geometry questions for CAT

Q-Consider obtuse-angled triangles with sides 8 cm, 15 cm, and x cm. If x is an integer, then how many such triangles exist?

(A)5
(B)21
(C)10
(D)15
(E)14

Solution: The correct option is C.

Let the three sides of the triangle be 8 cm, 15 cm, and x cm. As 15 is greater than 8, hence either x or 15 will be the largest side. Therefore, there will be the following 2 cases:

geometry questions for CAT

geometry questions for CAT

The triangle will be obtuse for all values of x<12.68. But as the sum of two sides of a triangle must be greater than the third side hence (x+8)>15 or x>7. Thus the permissible values of x are 8,9,10,11 and 12.

Check CAT Section-wise Preparation Tips.

 

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FAQs

  • Geometry is an important part of the Quantitative ability section of the CAT exam. As per CAT 2021 Exam Analysis, the candidates can expect 3-4 CAT Geometry Questions. Usually, 3-4 questions are asked each year in the CAT exam from the Geometry section which includes circles, triangles, etc.

  • Geometry questions for CAT consist of topics such as lines and angles, trigonometry, triangles, circles, polygons, squares, etc. the candidates must note that there is no defined Syllabus for CAT, so to ace Geometry Questions for CAT, must study all the related topics.

  • As per expert analysis, trigonometry is included in the CAT Geometry Question. It is an important part of CAT Geometry and if prepared well, then the candidates can get full marks from this section. So, focus on all important formulas and shortcut tricks to ace these questions.

  • It can not be said as everyone has a different level of understanding. However, as per expert analysis, the candidates can get easy to moderate difficulty level Geometry Questions for CAT. So, the main thing is that you have to be well-versed with all the important formulas with regular practice to solve these questions accurately.

  • As the expert opinion, the importance of CAT Geometry Questions is related to our real life. It helps us to decide the structure while making anything. The CAT Exam Authority has included this part in Quants to evaluate candidates’ numerical skills, as this skill is important to get the managerial designation in top MNCs.

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