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# Geometry Questions for SSC Exams 2023: Syllabus, Concept, Notes

By BYJU'S Exam Prep

Updated on: September 25th, 2023

**Geometry Questions for SSC Exam 2023: **The most well-known exam for candidates seeking government employment are SSC Exam. There are different subjects asked in the SSC Exam namely, English, Maths, Reasoning, etc., and the most crucial subject of the SSC Exams is Maths. One of the most important, high-scoring, and yet most despised topics in the SSC Exams’ Maths section is Geometry. Therefore, the significance of **geometry questions for SSC CGL**, CHSL, MTS, Stenographer, etc is obvious and doesn’t require a lengthy introduction.

In this article, we are going to provide you with all the important details about SSC Geometry like important **Geometry Questions for SSC CGL,** previous year questions, syllabus, theorems, important Geometry Topics for SSC CGL, etc.

Table of content

## SSC Geometry

Despite the fact that SSC geometry questions are crucial, due to the extensiveness of the syllabus, candidates sometimes ignore geometry. Additionally, Geometry for the SSC exams is only an extension of what we learned up till Class 10. Consequently, if handled systematically, this subject can be easily prepared in a few months. Let us take a look at the **SSC Geometry topics.**

- Basics of Geometry
- Polygons
- Triangle
- Circle
- Quadrilateral
- Mensuration 2D and 3D
- Miscellaneous

## Geometry for SSC CGL

SSC CGL Geometry Syllabus is very vast, and aspirants should know the major topic that has been asked in the CGL exam over the years. Listed below are a few important SSC CGL Geometry topics that one must study if he aims to crack the SSC CGL in the first attempt.

**Basics of Geometry****Polygons****Triangle****Circle****Quadrilateral****Miscellaneous (Covering Mensuration)**

If you understand the fundamentals of the topics described above, they are simple. To answer their questions more effectively, you must thoroughly grasp the concepts. Most of the SSC CGL Geometry questions will be based on figures therefore, understand all the laws and theorems. You should have information on your tips about angles, lines, chords, tangents, different kinds of triangles, etc.

## SSC CGL Geometry Syllabus

For your reference, a systematic and detailed SSC CGL Syllabus for Geometry is provided below. Candidates are advised to go through the detailed SSC CGL Geometry Syllabus to kickstart their preparation for SSC CGL 2023.

- Comprehending the basic concepts of SSC CGL Geometry
- Understanding the base-level concepts of geometry itself
- An introduction to Parallel lines
- An introduction to triangles
- Concepts and theorems of triangles
- Basic concept of Orthocentre
- Questions on Triangles
- Basic concepts of similar and congruent triangles
- Concepts of similar triangle theorems
- An introduction to quadrilaterals
- Questions related to Rhombus and Trapezium
- Basic concepts of Trapezium
- Basic concepts of Polygons
- An introduction to Circles
- Basic concepts of chords
- Important theorems pertaining to Circles
- Important SSC CGL Geometry questions covering circles

## Geometry Questions for SSC CGL

Solving SSC CGL Previous Year Question Paper is one of the best ways to be cognizant of the types of questions asked and know your weak areas. Also, if you are lucky enough, then you might see a few questions getting repeated with a sight modification! Take a look at the important SSC CGL Geometry Previous Year Questions listed below.

### SSC CGL Geometry Questions

1. The radii of two circles are 4 cm and 3 cm, respectively. What is the diameter (in cm) of the circle having an area equal to four times the sum of the areas of the two circles?

A. 12

B. 20

C. 24

D. 10

Answer ||| B

2. In the following figure, MN is a tangent to a circle with centre O at point A. If BC is diameter and ∠ABC = 42°, then find the measure of∠MAB.

A. 84°

B. 48°

C. 42°

D. 45°

Answer ||| B

3. In a ΔABC, D, E and F are the mid-points of side BC, CA and AB, respectively. If BC = 14.4 cm, CA = 15.2 cm and AB = 12.4 cm, what is the perimeter (in cm) of the ΔDEF?

A. 42

B. 28

C. 21

D. 35

Answer ||| C

4. PQ and RS are two parallel chords of a circle of length 14 cm and 48 cm, respectively, and lie on the same side of the centre O. If the distance between the chords is 17 cm, what is the radius (in cm) of the circle?

A. 28

B. 24

C. 25

D. 20

Answer ||| C

5. In Δ ABC, the perpendicular drawn from A, B and C meet the opposite sides at points D, E and F, respectively. AD, BE and CF intersect at point P. If ∠EPD= 110° and the bisectors of∠Aand∠Bmeet at point Q, then

∠AQB= ?

A. 115°

B. 110°

C. 135°

D. 125°

Answer ||| D

6. In the following figure, AD bisects angle BAC. Find the length (in cm) of BD.

A. 4

B. 5

C. 9

D. 6

Answer ||| A

7. AB is the diameter of a circle with centre O. C and D are two points on the circle on either side of AB, such that ∠CAB= 52° and∠ABD= 47°. What is the difference (in degrees) between the measures of∠CADand∠CBD?

A. 10

B. 15

C. 25

D. 20

Answer ||| A

8. AB and CD are two chords in a circle with centre O and AD is the diameter. When produced, AB and CD meet at the point P. If ∠DAP= 27°,∠APD= 35°, then what is the measure (in degrees) of∠DBC?

A. 28

B. 26

C. 30

D. 32

Answer ||| A

9. The radii of two concentric circles with centre O are 26 cm and 16 cm. Chord AB of the larger circle is tangent to the smaller circle at C and AD is a diameter. What is the length of CD?

A. 42 cm

B. 36 cm

C. 35 cm

D. 38 cm

Answer ||| D

10. In triangle ABC, the bisector of angle BAC meets BC at point D in such a way that AB= 10 cm, AC = 15 cm and BD = 6 cm. Find the length of BC (in cm).

A. 17

B. 11

C. 15

D. 9

Answer ||| C

### Geometry Questions for SSC CHSL

1. The perimeters of two similar Δ ABC and Δ PQR are 48.4 cm and 12.1 cm, respectively. What is the ratio of the area of Δ ABC and Δ PQR?

A. 4:1

B. 1:16

C. 16:1

D. 1:4

Answer ||| C

2. AB is a chord of a circle with centre O. C is a point on the circle in the minor sector. If ∠ABO= 50°, then what is the degree measure of∠ACB?

A. 100°

B. 130°

C. 110°

D. 140°

Answer ||| D

3. In a triangle ABC, points P and Q are on AB and AC, respectively, such that AP = 4 cm, PB = 6 cm, AQ = 5 cm and QC = 7.5 cm. If PQ = 6 cm, then find BC (in cm).

A. 10

B. 9

C. 15

D. 12

Answer ||| C

4. In a circle with centre O, PQ and QR are two chords such that ∠PQR= 118°. What is the measure of∠OPR?

A. 36°

B. 26°

C. 31°

D. 28°

Answer ||| D

5. A triangle with the lengths of its sides proportional to the number 7, 24 and 30 is:

A. acute angled

B. obtuse-angled

C. not possible

D. right-angled

Answer ||| B

6. In a right triangle ABC, right-angled at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6 cm, CD = 5 cm, then find the value of AB^{2} + BD^{2} (in cm^{2}).

A. 30

B. 96

C. 36

D. 66

Answer ||| B

7. In a triangle ABC, the bisector of angle BAC meets BC at point D such that DC = 2BD. If AC – AB = 5 cm, then find the length of AB (in cm).

A. 10

B. 12

C. 7

D. 5

Answer ||| D

8. In a circle with a centre O and of radius 13 cm, two parallel chords are drawn on different sides of the centre. If the length of one chord is 10 cm and the distance between the two chords is 17 cm, then find the difference in lengths of the two chords (in cm).

A. 10

B. 14

C. 24

D. 12

Answer ||| B

## Importance of SSC CGL Geometry Questions

As per the SSC CGL Previous Year Question Paper trends, the commission generally asks around 5 to 6 questions from this topic. Hence, candidates must not skip this topic and should familiarise themselves with the SSC CGL Geometry questions. Below, we have explained the concepts of geometry questions which will help you clear your doubts and improve your performance.

## Important Theorems in Geometry for SSC

### SSC CGL Geometry Concepts: Important Theorems and Properties of Circle

**Let the radius of circle is ‘R’, diameter = D**

(1) **Maximum area of triangle = R ^{2}**

If the given triangle is right angle triangle and its base is the diameter of the circle. Then, the maximum possible area of the triangle will be R^{2}.

(2) If AB and CD are two chords intersecting each other at P.

(3) If PA and PB are two tangents and LM is the tangent intersecting both tangents PA and PB as given in the figure.

Then, PA = PB = 1/2 Perimeter of triangle PLM.

(4) If BA is a chord intersecting tangent T at P as in the below figure.

Then, PA x PB = PT^{2}

5. This property is an important property of circle. It will help you to save your time in the exam. But don’t confuse between figure 5(a) and 5(b).

If angle AOC is x^{0} and BOD is y^{0}, then angle APC and BPD will be equal to half of the sum of both angle x^{0 }and y^{0}.

Fig. 5 (a)

If angle AOC is x^{0} and BOD is y^{0}, then angle APC and BPD will be equal to half of difference of the angle x^{0 }and y^{0}.

Fig. 5 (b)

(6) Quadrilateral formed by angle bisectors of a cyclic quadrilateral will be always a cyclic quadrilateral.

If given quadrilateral ABCD is a cyclic quadrilateral and RA, RB, PC and PD are angle bisectors of angle A, B, C and D. Then, quadrilateral PQRS formed by these angle bisectors will also be a cyclic quadrilateral.

Properties of Cyclic Quadrilateral:

1. The sum of diagonally opposite angle will always be equal to 180^{0}.

PQRS is also a cyclic quadrilateral.

(7) In the given diagram, ABCD is a cyclic quadrilateral.

If AB is parallel to CD, and AD is parallel to BC then, diagonals AC and BD will also equal.

(8) Tangents

(a) If there are two circles which are **at a distance apart** from each other, then the maximum possible number of common tangents are 4.

Fig. 8 (a)

(b) If there are two circles **touching each other externally**, then the maximum number of possible common tangents are 3.

Fig. 8 (b)

(c) If there are two circles** intersecting each other**, then the maximum number of possible common tangents are 2.

Fig. 8 (c)

(d) If there are two circles touching **each other internally**, then the maximum number of possible common tangents are 1.

Fig. 8 (d) No. of common tangents = 1

(e) If there are two circles, either concentric or one is inside the another and do not touch.

then, the number of common tangents will be zero.

Fig. 8 (e) No. of common tangents = 0

(9)

(a) If PA and PB are two tangents from P on the circle at A and B.

then, PA = PB

(b) The line joining the centre and the point on the circle at which tangent meets will always be perpendicular to the tangent.

(10) If the tangent PAQ and chord AB makes an angle θ, then the angle made by chord AB on the circle will always be θ.

Similarly, If the tangent PAQ and chord AC makes an angle ϕ, then the angle made by chord AC on the circle will always be ϕ.

(10) If AB, BC, CD and AD are tangents on circle as given in the diagram,

Then AB + CD = BC + AD

(11) The distance between centres of two circles.

(a)

distance b/w centres = r_{1} – r_{2}

(b)

distance b/w centres = r_{1} + r_{2}

(12) **Length of Direct Common Tangent**.

If ‘d’ is the distance between centres of two circles and r_{1 }and r_{2 }are the radius of given two circles.

or

Fig. 12 (a) Fig. 12 (b)

**Transversal common tangent**

**Note:** Do not confuse between transversal and direct common tangent.

(12). This question is asked many times in SSC Exams. Remember the diagram as it is given, all three circles have a direct common tangent.

(13)

If PQ is diameter and PR||QS

Then, PQ = RS and

(14) If ABCD is a cyclic quadrilateral and angle APC is x^{0}, then angle ADC = 90^{0} – x/2 and angle ABC = 90^{0}+x/2.

(15) If AB, BC, CD and AD are tangents on the given circle, then x^{0}+y^{0} = 180 degree.

(16) If you find such diagram and angle ADB = x^{0} then angle ACB = 180^{0} -x^{0}.

(17) If AB is the diameter of the bigger circle and ‘r’ is the radius of the smaller circle.

A B

(18) If AB is the tangent of two circles at A and B, P is the point at which both circles meet. Then, angle APB will be 90^{0}.

(19) If there are two circles of **same radius ‘R’** and the **distance between their centres is ‘R’.**

Then, the length of common chord CD = √ 3 R.

**20. How to find the distance between two chords?**

(a) If chords are on the opposite sides of centre

Let ‘a’ and ‘b’ are the length of chords and ‘d’ is the distance between them.

If it follows this relation,

Then, we can say that

(b) If chords are on the same side of centre

Let ‘a’ and ‘b’ are the length of chords and ‘d’ is the distance between them.

If it follows this relation,

Then, we can say that

## Best Book to Prepare for Geometry Questions for SSC CGL

Below are the important SSC CGL books for Geometry that an aspirant must have for the complete preparation of the SSC CGL Geometry section for the upcoming SSC CGL 2023 examination.

- Magical Books On Quicker Maths by M-Tyra (BSC publication)
- SSC Mathematics 5800+ by Kiran Publication
- Online Quiz (thousands of questions to practice are available) by BYJU’S Exam Prep

### Things to Remember while attempting SSC Geometry Questions

- Don’t attempt the questions until you have completely read them.
- Don’t make any guesses. Negative marking is there, so if you are not confident about any question, then don’t waste your time to solve it as it will only waste your time and deduct your marks.
- Don’t spend more time than the allotted time.

That’s all you need to know about geometry for SSC CGL. If you have any queries, you can comment below.

**All The Best !!!**

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