Most Important CAT Geometry Questions 2025 with Solutions PDF Download

Overview: Geometry is important for the CAT exam 2025. With dedicated preparation, you can handle CAT Geometry Questions proficiently. Read on to get the 30+ most important CAT geometry questions to boost your practice!

• Geometry is one of the key topics of the Quantitative Aptitude Section of the CAT. Questions in this area are based on two-dimensional, three-dimensional, coordinate, and other related topics. 

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• Practising CAT geometry questions daily is the best way to get good scores in this section. For this you should have a good understanding of the fundamental geometric formulas and advanced techniques.

Scroll down to get the CAT geometry questions to practice now!

 Read more: Syllabus for CAT Exam 2025

Formulas For CAT Geometry Questions 2025

Here are some important formulas to use in geometry CAT level questions:

Basic Shapes In Geometry CAT Level Questions

• • TriangleArea: A = 1/2 * base * height
  • Perimeter: P = base + side + side (where base and side represent the lengths of the triangle's sides)
• • RectangleArea: A = length * width
  • Perimeter: P = 2(length + width)
• • SquareArea: A = side² (where side represents the length of a square's side)
  • Perimeter: P = 4(side)
  • CircleArea: A = πr² (where π is a constant value approximately equal to 3.14 and r represents the circle's radius)
  • Circumference: C = 2πr

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Lines and Angles In Geometry CAT Level Questions

• Straight Angle: measure is 180 degrees
• Right Angle: measure is 90 degrees
• Complementary Angles: two angles that add up to 90 degrees
• Supplementary Angles: two angles that add up to 180 degrees

Theorems For Geometry And Mensuration Questions For CAT

• Pythagorean Theorem: a² + b² = c² (where a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse)

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CAT Geometry Questions 2025

Ques.1  x, y, z are integers representing the sides of an obtuse-angled triangle. If xy = 4, find z.

1. 2
2. 3
3. 1
4. More than one possible value of z exists

Answer: 1

Ques.2   The triangle's perimeter is 6 + 2√3. One angle in the triangle equals the exterior angle of a regular hexagon, while another angle equals the exterior angle of a regular 12-sided polygon. Please find the area of the triangle.

1. 2√3
2. √3
3. √3/2
4. 3

Answer: 2√3

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Ques.3 ABCD, a rhombus, has diagonals AC and BD intersecting at the origin on the x-y plane. The equation of the line AD is x + y = 1. What is the equation of line BC?

1. x + y = –1
2. x – y = –1
3. x + y = 1
4. None of these

Answer: x + y = –1

Ques.4  Chords AB and CD intersect at point P at right angles. The length of segment AP is 4 units, while the length of segment PB is 6 units, and the length of segment CP is 3 units. Determine the radius of the circle.

1. 31.25^(1/2)
2. 37.5^(1/2)
3. 26^(1/2)
4. 52^(1/2)

Answer: 31.25^(1/2)

Explore: Important CAT Quantitative Aptitude Questions

Ques.5  An equilateral triangle contains a square inscribed within it, where one side of the square lies along a side of the equilateral triangle. What is the ratio of the area of the square to the area of the equilateral triangle?

1. √3 : (5 + 4√3)
2. 2√3 : (7 + 4√3)
3. 4√3 : (7 + 4√3)
4. 4√3 : (5 + 2√3)

Answer: 4√3 : (7 + 4√3)

Ques.6 A farmer plans to erect a wire fence along one straight side of his property by placing several fence-posts at 6 m intervals, with posts fixed at both ends of the side. However, after purchasing the posts and wire, he realized that he had bought 5 fewer posts than required. Yet, he found that the number of posts he had bought would be just enough if he spaced them 8 m apart. The question is, what is the length of the side of his property and how many posts did he buy?

1. 100 m, 15
2. 100 m, 16
3. 120 m, 15
4. 120 m, 16

Answer: 120 m, 16

Ques.7 A city contains two fully circular and concentric ring roads. The outer ring road (OR) is twice as long as the inner ring road (IR). There are also four straight chord roads: from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR to S2, the south end point of IR; and from S1, the south end point of OR to E2, the east end point of IR. Vehicles move at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and 15 5 km/hr on all the chord roads. Amit wants to travel from N1 to E2 using the N1 – W2 chord road and then the inner ring road. What will be his traveling time in minutes based on the information given in the question above?

1. 60
2. 45
3. 90
4. 105

Answer: 105

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Ques.8 Please remember the following information. The question requires a response based on the following instructions.

ABC Corporation must have a minimum of 400 Kilolitres of water at all times in its factory to comply with safety and regulatory standards. ABC is assessing the appropriateness of using a spherical tank with uniform wall thickness for this purpose. The external diameter of the tank is 10 meters. Is the tank capacity sufficient to meet ABC’s requirements?

Statement A: The tank's internal diameter is at least 8 meters.

Statement B: The tank weighs 30,000 kg when empty and is constructed of a material with a density of 3 gm/cc.

1. The questions can be answered using A alone but not using B alone.
2. The question can be answered using B alone but not using A alone.
3. The question can be answered using A and B together, but not using either A or B alone.
4. The question cannot be answered even using A and B together

  Answer: The question can be answered using B alone but not using A alone.

Ques.9 The given problem deals with two circles having centers O1 and O2, and these circles touch each other externally at a point R. There is a tangent, AB, that touches both circles passing through R. Another tangent, P’Q’, touches the circles at P and Q, and intersects AB at point S. The length of PQ is 6 cm, and the distances of point S from the centers of the circles are 5 cm and 4 cm. We need to find the area of the triangle SO1O2.

1. 9 cm^2
2. 3(4+√7)/2 cm^2
3. 27/2 cm^2
4. (3√41)/2 cm^2

Answer: 3(4+√7)/2 cm^2

Ques.10 The third side of a triangle with 8 cm and 9 cm as its two sides and one angle of 60∘ could have which of the following lengths?

I. √23 cm

II. √73 cm

III.(4.5 - √3.25) cm

IV. (4 + √33) cm

V. (9 + √13) cm

1. Only II and IV
2. Only I and III
3. Only I, II and V
4. Only II, III and IV

Answer: Only II, III and IV

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Ques.11 A right-angled triangle PQR is given, where the angle PRQ measures 90 degrees and the length of QR is 4 centimeters. T is a point on QR, with PT measuring 3 centimeters. The perimeter of triangle PQT is equal to the perimeter of triangle PTR. Therefore, we need to find the value of QT/TR.

1. QT/TR < 1/3
2. 1/3 < QT/TR < 1
3. QT/TR > 1
4. can’t be determined

Answer: 1/3 < QT/TR < 1

Ques.12 The number of diagonals in a regular polygon is multiplied by ‘T’ to get the number of sides. What is the interior angle of this polygon expressed in terms of T?

1. 180 * (T+2)/(3T+2)
2. 540 * (T+2)/(3T+2)
3. 360 * (T+2)/(3T+2)
4. 90 * (T+2)/(3T+2)

Answer: 180 * (T+2)/(3T+2)

Ques.13 Consider the following information: Let triangle △ABC be an isosceles triangle with the property that AB and AC are equal in length. The altitude from A to BC is denoted as AD, and the altitude from B to AC is denoted as BE. These altitudes intersect at point O, where ∠AOB measures 105 degrees. What is the ratio of AD to BE?

1. 2sin15∘
2. cos⁡15∘
3. 2cos⁡15∘
4. sin15∘

Answer: 2cos⁡15∘

Ques.14 The following text should be remembered:

A rectangular area has a length of 40 meters and a width of 30 meters. Diagonals should be drawn in this area, and then circles, each with a radius of 1.25 meters. The circles' centers should only be located on the diagonals, and each circle must fit entirely within the area. While the circles can touch each other, they should not overlap.

What is the maximum number of circles that can be drawn in the area?

1. 39
2. 40
3. 37
4. 36

Answer: 37

Ques.15 An equilateral triangle, XYZ, is inscribed within a circle. Point P lies on the arc YZ in such a way that point X and P are on opposite sides of chord YZ. We need to determine which statement among the options must always be true.

1. XZ + YP = XY + PZ
2. XP = YP + PZ
3. XP + PZ = XY + YP
4. XP = XY

Answer: XP=YP+PZ

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Techniques To Solve CAT Geometry Questions 2025

The CAT exam is all about efficiency. While getting the perfect answer is ideal, there are situations where estimation can be your best friend, especially in the coordinate geometry CAT Questions section. Here's how estimation techniques can help you conquer CAT geometry:

• Round Numbers: Round off measurements in the coordinate CAT geometry questions to nearby whole numbers or easy fractions. This simplifies calculations and provides a reasonable estimate.
• Proportions: Analyze the problem visually. Are there similar shapes or ratios you can use to estimate side lengths or areas?
• Dimensional Analysis: Identify the units involved (length, area, volume) and see if the answer choices make sense dimensionally. Eliminate options with units that wouldn't result from the given problem.
• Grid Method: For area and perimeter problems involving squares or rectangles, imagine a grid overlaying the shape. Estimate the number of grid squares covered and use that to approximate the area or perimeter.
• Reference Points: Use properties of common shapes as reference points. For instance, the diameter of a circle is twice its radius.

Example:

A square has a diagonal that is √2 times its side length. What is the approximate area of the square?

Options:

(a) 1 (b) 2 (c) 4 (d) 8 (e) 16

Estimation Approach:

We know the diagonal of a square is longer than its side. √2 is roughly 1.4. Squaring this value (1.4² ≈ 2), we can estimate the area to be around 2 times the square of the side length.

Looking at the options, only (b) - 2 - seems reasonable based on our estimation.

Remember: Estimation provides an approximation, not an exact answer. However, it's a powerful tool for CAT geometry previous year questions, allowing you to save time and make informed decisions during the exam.

Bonus Tip: Practice estimation techniques with mock tests and CAT geometry previous year questions. The more you practice, the more comfortable and confident you'll become in using estimation effectively.

Read more:  CAT PI Questions with Answers

Tips to Solve CAT Geometry Questions 2025

Mastering the geometry and mensuration questions for CAT exam can be challenging, but with the right strategy, you can overcome it. Here are some recommendations to effectively tackle geometry and mensuration questions for CAT:

1. Grasp the Basics: Understanding fundamental geometric cat level questions such as lines, angles, triangles, circles, quadrilaterals, and their properties is essential.
2. Formula Knowledge: Familiarize yourself with important geometric and mensuration questions for CAT formulas for calculating areas, perimeters, volumes, and other relevant measurements.
3. Save Precious Time: Sometimes, intricate calculations can eat away at valuable time. Estimation allows you to quickly get a ballpark figure for the answer, letting you move on to other questions.
4. Eliminate Wildly Incorrect Options: By estimating, you can identify answer choices that are way off the mark. This narrows down your options and increases your chances of picking the correct answer, even if you don't have time for a full calculation.

Conclusion

Remember, a solid understanding of the core concepts is the key to success in geometry cat level questions. Practice with a variety of cat geometry questions with answers to hone your skills and reinforce your confidence. By persistently practicing and applying the strategies explained in this blog, you'll be well-prepared to tackle the geometry questions with answers and move closer to your academic goals.

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