# 15+ CAT Previous Year Geometry Questions: 2021, 2020, 2019, and 2018 (Download Geometry Formulas PDF)

The majority of the CAT Previous Year Geometry Questions are based on concepts like triangles, quadrilaterals, and circles. To understand and attempt geometry questions, candidates must be well-versed in all the complex ideas and theorems related to the subject of geometry. The CAT Quant section is one of the hardest sections to prepare. It takes constant practice to master time management and concepts. Based on past exam trends, we have listed below a few questions.

## CAT Previous Year’s Geometry Questions: 2021, 2020, 2019, 2018

Here are a few questions listed below for your easy reference for the previous years:

### CAT Geometry Questions 2021

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

A)4√6

B)6√6

C)√6

D)2√6

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

A) 4√6

B) 6√6

C) 2√6

D) √6

Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. If T is the midpoint of CD, then the length of AT, in cm, is

A) 6√6

B) 2√6

C) √13

D) 6√6

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

A) 4√6

B) 2√6

C) 6√6

D) 2√6

### CAT Geometry Questions 2020

Let C1 and C2 be concentric circles such that the diameter of C1 is 2cm longer than that of C2. If a chord of C1 has a length 6 cm and is tangent to C2, then the diameter, in cm of C1 is

A) 12

B) 9

C) 8

D) 10

Let C be a circle of radius 5 meters having centre at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

A) 12

B) 9.8

C) 5.5

D) 8.8

From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is ‘s’. Then the area of the triangle is:

A) s22√3

B) 2s2√3

C) √3s22√3s22

D) s2√3

### CAT Geometry Questions 2019

AB is the diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to

A) 8.5

B) 9.3

C) 9.1

D) 7.8

In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is

A) 80

B) 90

C) 72

D) 78

Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is

A) π / 3

B) 1 / √2

C) 1

D) √2

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular to BC, then the maximum possible length of AP, in cm, is

A) 5

B) 10

C) 6√2

D) 8√2

### CAT Geometry Questions 2018

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,… will be

A) 192√3

B) 248√3

C) 188√3

D) 164√3

In a circle with centre O and a radius of 1 cm, an arc AB makes an angle of 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is

A) (π / 4)1 / 2

B) (π / 4√3)1 / 2

C) (π / 3√3)1 / 2

D) (π / 6)1 / 2

Correct Answer: (π / 6)1 / 2

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,… will be

A) 192√3

B) 164√3

C) 188√3

D) 248√3

Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?

A) 25, 10

B) 24, 12

C) 24, 10

D) 25, 9

The base of a vertical pillar with a uniform cross-section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

A)1300

B)1480

C) 1520

D) 1620

A circle of diameter 8 inches is inscribed in a triangle ABC where∠ABC=90∘. If BC = 10 inches then the area of the triangle in square inches is?

A)133

B)120

C)145

D) 146

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

A)245

B)√13

C)√67

D)√12

## FAQs

Q1. Is geometry in CAT difficult?

Ans: The difficulty level of these questions is usually easy to moderate; however, conceptual clarity is the key to solving CAT Geometry Questions accurately and quickly.

Q2. Does previous year questions are repetitive in CAT?

Ans: In top MBA exams such as NMAT, SNAP, CMAT and CAT, questions from previous years may not be directly repeated.

Q3. How many questions come from geometry in the CAT exam?

Ans: Candidates can expect around 3-4 geometry questions as it is an important part of the quantitative section.

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