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
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?
(C)
(D)
(E)
Solution: The correct option is E.
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)
(B)
(C)
(D)
(E)
Solution: The correct option is E.
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:
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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