Geometry Questions for CAT – Concepts, Important Formulae, Download Sample Questions PDF

What are Geometry Questions for CAT?

Considering the previous year’s CAT Exam Analysis, it is seen that geometry questions consist of questions related to both geometry and mensuration. So the candidates must be aware of CAT Geometry and Mensuration Formulas to solve these questions efficiently and accurately. It is one of the most important topics for CAT Quant Questions. As per the trends, you can expect 3-4 Geometry Questions for CAT, consisting of concepts that the candidate must have studied in high school.

The difficulty level of Geometry Questions for CAT is usually Easy to Moderate. If the candidates prepare all the important formulae, then they can easily solve these questions and get a good CAT Percentile in this section. Note the section below to get all the necessary information related to Geometry CAT Questions.

Topics Covered in Geometry Questions for CAT

The candidates aiming at the upcoming CAT must study the important topics and formulas 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, and Rectangle. Square, Rhombus, Trapezoid, etc.
• Special Triangle
• Circumradius and Inradius
• Similar and Congruent Triangle
• Volume, Total Surface Area, and Lateral Surface Area of Different Solids like Cubes, Cuboids, Cylinders, Pyramids, Cones, Spheres, Hemispheres, and Frustum

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

Geometry for CAT PDF

The candidates need to be comfortable with the types of Geometry Questions for the CAT Exam. It is imperative 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 can understand the types and difficulty levels of these questions.

☛ Download Geometry CAT Questions PDF

Previous Year Geometry Questions for CAT

Q1- 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

 

Q2- Consider a square ABCD with midpoints E, F, G, and 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) (4√2)/3

(B) 2 + √3

(C) (10 – 3√3)/9

(D) 1+ 1/√3

(E) 2√3 – 1

Solution: The correct option is E.

 

 

 

Q3- 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) π/3 – √3/4

(B) 2π/3 + √3/2

(C) 4π/3 – √3/2

(D) 4π/3 + √3/2

(E) 2π/3 – √3/2

Solution: The correct option is E.

 

Q4- 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:

 

 

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.

CAT Geometry Questions Formulae

Geometry is a part of the CAT Quantitative Aptitude Section that consists of several formulas and theorems. So, it is extremely important to prepare these formulas and theorem to easily solve and score well in all Geometry Questions for CAT. Below are some of the formulas related to CAT Geometry Questions:

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 centre 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 most important step to solve CAT Questions on Geometry is the candidates must have good knowledge of the type of Geometry Questions for CAT and its related formulae. Below are some expert-recommended tricks that you can follow to solve Geometry CAT Questions.

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

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