# Geometry

Geometry, often seen as a labyrinth of shapes and angles, is your essential passport to CAT exam success. At Quantifiers, we’re here to make geometry not just understandable but also a fascinating journey. Join us as we explore the intricate world of geometry and discover how it can open doors to your CAT exam triumph!

## Understanding Geometry​

Before we dive into the CAT exam specifics, let’s embark on a journey through the world of geometry. Geometry is like the art of shapes and spaces, offering a toolkit to explore and understand the physical world. It’s the science of visualizing, measuring, and relating objects and their properties.

Let’s connect the dots between geometry and the CAT exam. Geometry plays a pivotal role in the Quantitative Aptitude section, and here’s why it’s indispensable:

• Logical Problem Solving: Geometry questions in the CAT exam test your logical and analytical thinking. They challenge you to apply geometric concepts to solve real-world problems.

• Data Interpretation: Geometry often appears in data interpretation problems, where you’ll need to analyze charts, graphs, and diagrams, making accurate measurements and inferences.

• Geometric Series and Progressions: Understanding geometric progressions is fundamental for cracking certain types of questions in the CAT exam, especially in quantitative analysis.

Mastering geometry is not just about conquering the CAT exam; it’s about developing your problem-solving skills, spatial reasoning, and critical thinking, all of which are invaluable in numerous aspects of life. Join Quantifiers today, and turn geometry into your ticket to explore new horizons on the path to mastering the CAT exam!

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## Practice Questions for CAT with Solutions

### 1. CAT - Geometry

The length of the line joining the midpoints of the non-parallel sides of an isosceles trapezium is 24. If the aforementioned line divides the trapezium in two parts with the areas in ratio 7: 9, then what is the absolute difference (in cm) between the parallel sides of the trapezium?

12

### 2. CAT - Geometry

P is any point inside triangle ABC such that PA = 5 units, PB = 6 units and PC = 8 units. Also ∠APB=120 degree and ∠APC=150 degree. The approximate perimeter of triangle ABC is:

1. 32 Units

2. 68 Units

3. 50 Units

4. 48 Units

1. 32 Units

### 3. CAT - Geometry

AF bisects angle EAD in a square ABCD, if FD = 64 cm, and BE = 36 cm, find AE.

100

### 4. CAT - Geometry

A square ABCD with side 8 has point E on AD, the value of BE+CE is definitely greater than:

1. 8√5

2. 8√6

3. 8√7

4. CBD

1. 8√5

### 5. CAT - Geometry

3 altitudes of triangle PQR have lengths 4,6 and 8 respectively, If P PQR has in-radius of length y, find 13y

24

### 6. CAT - Geometry

ABC is an equilateral triangle with O a point in it, with AO, BO and CO being 6,8,10. If triangle has an area of a√3 + b, find a+b.

60

### 7. CAT - Geometry

In a triangle ABC, AB = 60, BC= 80, CA= 100. D is a point on AC such that perimeters of triangles ABD and CBD are equal. If the length of BD is AV5, find the value of A.

24

### 8. CAT - Co-ordinate Geometry

Let P be the point of intersection of the lines 3x + 4y = 2a and 7x + 2y = 2018 and Q the point of intersection of the lines 3x + 4y = 2018 and 5x + 3y = 1. If the line through P and Q has slope 2, the value of a is:

1. 1

2. 1/2

3. 4035

4. 1009

5. 3026

5. 3026

### 9. CAT - Geometry

A triangle has its longest side as 38 cm. If one of the other two sides is 10 cm and the area of the triangle is 152 sq.cm, and the length of the third side is AVB,find the value of A+B .

25

### 10. CAT - Geometry

The length of sides AB, BC and CA of a triangle ABC is 7 cm, 10 cm and 12 cm respectively. AB is extended to D such that AD = 28 cm. BC is extended to E such that BE = 20 cm. CA is extended to F such that CF = 36 cm. What is the ratio of the area of triangle ABC to the area of triangle DEF?

1 : 18

### 11. CAT - Geometry

PQR is a right angled triangle where angle R is 90 degree. S is a point on PQ such that PS 29 and QS=1 and RS=13. Find area of triangle QRS.

6

### 12. CAT - Geometry

In the diagram, P,Q and R lie on a circle, the tangent at P and the secant QR intersect at T. The bisector of angle QPR meet at S so that QPS = RPS, If SQ=3 and PT = 4, Find length of RS

12/7

### 13. CAT - Geometry

In a triangle ABC side AC and the perpendicular bisector of side BC meet in point D and BD bisects angle abc. if ad is 9 DC is 7 find the area of triangle ABD

14√5

### 14. CAT - Geometry

A circle of diameter 8 inches is inscribed in a triangle ABC where angle ABC= 90 degree. If BC = 10 inches then the area of the triangle in square inches is:

120

### 15. CAT - Geometry

If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is:

1. 6√6

2. 2√6

3. √6

4. 4√6

2. 2√6

### 16. CAT - Geometry

Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. It T is the mod point of CD, then the length of AT, in cm, is:

1. √13

2. √15

3. √14

4. √12m

1. √13

### 17. CAT - Geometry

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is:

1. 40

2. 25

3. 20

4. 30

4. 30

### 18. CAT - Geometry

If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is:

1. √30 + √12

2. √37 + √13

3. (√13 + √12) / 2

4. (√37 + √13) / 2

2. √37 + √13

### 19. CAT - Geometry

Let ABCD is a parallelogram. The lengths of the sides AD and the diagonal AC are 10 cm and 20 cm, respectively. If the angle ADC is 30 degree, then the area of the parallelogram, in sq. cm, is

1. 25 (√5 + √15)

2. 25 (√3 + √15)

3. 25 (√5 + √15) / 2

4. 25 (√3 + √15) / 2

2. 25 (√3 + √15)

### 20. CAT - Geometry

A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is:

3500

### 21. CAT - Geometry

In a triangle ABC, angle BCA = 50 degree. D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then angle FDE, in degrees, is equal to

1. 72

2. 100

3. 96

4. 80

4. 80

### 22. CAT - Geometry

In ΔABC, ∠B = 900. PQRS is a square of side 5 units and WXYZ is a square of side 10 units. MS and SY are the length and breadth respectively of rectangle MNSY. What is the length of MS?

1. 12 cm

2. 15 cm

3. 25 cm

4. 20 cm

2. 15 cm

### 23. CAT - Geometry

The vertices of a triangle are (0, 0), and (4, 0) and (3, 9). The area of the circle passing through these three points is:

1. 12π/5

2. 14π /5

3. 205π/9

4. 123π /7

3. 205π  /9

### 24. CAT - Geometry

In triangle ABC, M is the midpoint of the side AB. N is point in the interior of aking triangle ABC, such that CN is the bisector of angle C and CN is perpendicular to NB. What is the area of triangle BMN and AMN if CN=6, BC= 10cm and AC = 15cm?

6

### 25. CAT - Geometry

In a triangle PQR, S is a point on QR and T is a point on PR such that PQ= PR and PS-PT.Angle QPS= 40 degrees. Find angle TSR

20

### 26. CAT - Geometry

BD and CE are the medians of triangle ABC, right angled at A. If CE=5V13/2 and BC=10 then length of BD is

5√7 / 2

### 27. CAT - Geometry

PQRS is an isosceles trapezium in which PQ is parallel to RS and X is the mid point of PS. If PX= 8 and angle QXR= 90 degrees. Fine the perimeter of the trapezium PQRS.

48

### 28. CAT - Geometry

Length of sides of two rhombuses differ by 2. One of the diagonals for each of the rhombuses is of the same length as that of its side. Product of their areas is 168.75. Find the side of smaller

3

### 29. CAT - Geometry

BD and CE are the medians of the triangle ABC right angled at A. If CE = 5√13/2 and BC = 10, then the length of BD is:

5√7 / 2

### 30. CAT - Geometry

If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is:

√37 + √13

### 31. CAT - Geometry

ABCD is a rhombus where E is a point on diagonal AC such that AC = 50 and AE = 41. Angle ABE = 90 degree. Find the area of rhombus.

1000

### 32. CAT - Geometry

Consider triangle with sides in the ratio 1: 1: √n and angles in the ratio 1: 1: m where m, n are distinct natural numbers. What is the value of m + n?

7

### 33. CAT - Geometry

In the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8, then the perimeter of the shaded part is:

3π + 10

### 34. CAT - Geometry

Product of two sides of a triangle is 6. If all three sides are having integral value, then how many such obtuse angle triangles are possible?