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SSC CGL Exam  >  SSC CGL Test  >  Quantitative Aptitude  >  MCQ: Circles - 2 - SSC CGL MCQ

Circles - 2 - Free MCQ Practice Test with solutions, SSC CGL Quant Aptitude


MCQ Practice Test & Solutions: MCQ: Circles - 2 (15 Questions)

You can prepare effectively for SSC CGL Quantitative Aptitude for SSC CGL with this dedicated MCQ Practice Test (available with solutions) on the important topic of "MCQ: Circles - 2". These 15 questions have been designed by the experts with the latest curriculum of SSC CGL 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

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MCQ: Circles - 2 - Question 1
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Directions: Kindly study the following questions carefully and choose the right answer:

In a right angled triangle, the circumcentre of the triangle lies.

Detailed Solution: Question 1

∠APB = 90°
AB = Diameter = Hypotenous of triangle APB
As, the angle of semicircle is right angle
so, the circumcentre lies on midpoint of hypoteneous
Hence, option (C) is correct.

MCQ: Circles - 2 - Question 2
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Directions: Kindly study the following questions carefully and choose the right answer:

In the given figure below, ∠AOB = 48° and AC and OB intersect each other at right angles.
What is the measure of ∠OBC? (O is the centre of the circle)

Detailed Solution: Question 2

∠AOB = 48°


(As angles made by same arc AB)
Given AC and OB intersect each other at right angle.
∠ CQB = 90°
∠ CBQ = 180° – (90° + 24°) = 66°
so , ∠ OBC = 66°
Hence, option B is correct

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MCQ: Circles - 2 - Question 3
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Directions: Kindly study the following questions carefully and choose the right answer:

The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles are 30 cm and 26 cm, then the distance between the centre (in cm) is

Detailed Solution: Question 3

Given, Common chord AB = 24 cm
Then, AD = DB = 12 cm
Diameter of circle of centre O = 30 cm, Then radius OA = 15 cm
And, Diamter of circle of centre O' = 26 cm, Then radius O'A = 13 cm
From ΔOAD, By pythagoras theorem

From ΔO'AD, By pythagoras theorem

Hence, option B is correct.

MCQ: Circles - 2 - Question 4
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Directions: Kindly study the following questions carefully and choose the right answer:

A unique circle can always be drawn through x number of given non-collinear points, then x must be

Detailed Solution: Question 4

A unique circle can always be drawn through x number of given non-collinear points, then x must
be.
Hence, option B is correct.

MCQ: Circles - 2 - Question 5
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Directions: Kindly study the following questions carefully and choose the right answer:

The length of the common chord of two circles of radii 30 cm and 40 cm whose centres are 50 cm apart, is (in cm)

Detailed Solution: Question 5

BD = 50 cm
Let, BC = x cm, then CD = (50 – x) cm
In ΔABC, By pythagoras theorem

In ΔACD, By pythagoras theorem

Hence, option D is correct.

MCQ: Circles - 2 - Question 6
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Directions: Kindly study the following questions carefully and choose the right answer:

The distance betwen two parallel chords of length 8 cm each in a circle of diameter 10 cm is

Detailed Solution: Question 6

Given, Chord AB = Chord CD = 8 cm
Then, AP = PB = 4 cm and Diameter = 10 cm, then radius = 5 cm
Note : Equal chords of a circle (or of congruent circles) are equidistant from the centre.
∴ OP = OQ
From ΔOAP, By pythagoras theorem

Hence, option A is correct.

MCQ: Circles - 2 - Question 7
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Directions: Kindly study the following questions carefully and choose the right answer:

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and distance between them is 17 cm, then the radius of the circle is :

Detailed Solution: Question 7

AB = 10 cm and CD = 24 cm
∴ AE = EB = 5 cm and CF = FD = 12 cm
EF = 17 cm
Let, EO = x cm, then OF = (17 – x) cm
In ΔAOE, By pythagoras theorem

In ΔCOF, By pythagoras theorem

52 + x2 = 122 + (17 – x)2
25 + x2 = 144 + 289 – 34x + x2
34x = 408
x = 12

Hence, option C is correct.

MCQ: Circles - 2 - Question 8
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Directions: Kindly study the following questions carefully and choose the right answer:

Two circles of same radius 5 cm, intersect each other at A and B. If AB = 8 cm, then the distance between the centre is :

Detailed Solution: Question 8

AB = 8 cm ⇒ AC = 4 cm
OA = 5 cm
In ΔAOC, By pythagoras theorem


Hence, option A is correct.

MCQ: Circles - 2 - Question 9
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Directions: Kindly study the following questions carefully and choose the right answer:

O and O' are respectively the orthocentre and circumcentre of an acute angled triangle PQR. the point P and O are joined and produced to meet the side QR at S. If ∠PQS = 60° and ∠QO'R = 130° then ∠RPS = ?

Detailed Solution: Question 9

∠ PQS = 60°
∠QO'R = 130°

⇒ ∠ QRP = 180° – 60° – 65° = 55°
⇒ ∠PO'Q = 110°
In Δ QO'R
QO' = O'R
⇒ ∠O'QR = ∠O'RQ = 25°
∵ ∠O'QR + ∠O'RQ = 50°
⇒ ∠PQO' + ∠QPO' = 35°
∵ ∠PQO' + ∠QPO' = 70°
Similarly, ∠O'PR = 30°
∴ ∠RPS = 35°
Hence, option (B) is correct.

MCQ: Circles - 2 - Question 10
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Directions: Kindly study the following questions carefully and choose the right answer:

In a circle of radius 17 cm, two parallel chords of length 30 cm and 16 cm are drawn. If both the chords are on the same side of the centre, then the distance between the chords is

Detailed Solution: Question 10

AB = 30 cm and CD = 16 cm
∴ AE = EB = 15 cm and CF = FD = 8 cm
Radii, OA = OC = 17 cm
In ΔAOE, By pythagoras theorem

Again In ΔCOF, By pythagoras theorem

Distance between chords, EF = OF – OE = 15 – 8 = 7 cm
Hence, option B is correct.

MCQ: Circles - 2 - Question 11
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Directions: Kindly study the following questions carefully and choose the right answer:

The length of two chords AB and AC of a circle are 8 cm and 6 cm and ∠BAC = 90°, then the radius of circle is

Detailed Solution: Question 11

∠BAC = 90°
As, BC is the diameter of the circle.

Hence, option D is correct.

MCQ: Circles - 2 - Question 12
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Directions: Kindly study the following questions carefully and choose the right answer:

Two circles touch each other internally. Their radii are 2 cm and 3 cm. The biggest chord of the greater circle which is outside the inner circle is of length

Detailed Solution: Question 12

O'A = O'C = O'D = 3 cm [∵ radii of a circle]
OA = OB = 2 cm
AC = 2 x OA' = 2 x 3 = 6 cm
AB = 2 x OA = 2 x 2 = 4 cm
BC = AC – AB = 6 – 4 = 2 cm
∴ O'B = O'C – BC = 3 – 2 = 1 cm
In ΔBDO', By pythagoras theorem


Hence, option D is correct.

MCQ: Circles - 2 - Question 13
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Directions: Kindly study the following questions carefully and choose the right answer:

PQ is a chord of a circle with centre O and SOR is a line segment originating from a point S on the circle and intersecting PQ produced at R such that QR = OS. If ∠QRO = 30° then ∠POS = ?

Detailed Solution: Question 13

Let radius be 'r' and ∠POS = x°
ΔOQR isosceles ∴∠QOR = 30°
∴ ∠OQR = 120° (Sum of all angles of ΔOQR = 180°)
∴ ∠OQP = 60° (Supplementary angle)
ΔOPQ isosceles since OP = OQ = r
∴ ∠OQP = 60° = ∠OQP
∴ ∠ POQ = 60° = [Sum of all angle of Δ = 180° ]
Now SOR is a straight line
∴ x + 60° + 30° = 180°
∴ x = 90°
Hence, option (C) is correct.

MCQ: Circles - 2 - Question 14
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Directions: Kindly study the following questions carefully and choose the right answer:

AB is the diameter of a circle with centre O and radius OD is perpendicular to AB. Find the angle BAD

Detailed Solution: Question 14

In Δ AOD :
OA = OD (radius)
∠ AOD = 90 ( as OD is perpendicular to AB )
So Δ AOD is isosceles having OA and OD sides equal and one angle as 90
So the remaining wo angles are 45 each
Hence ∠ BAD = 45°
Therefore, option (B) is correct.

MCQ: Circles - 2 - Question 15
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Directions: Kindly study the following questions carefully and choose the right answer:

In a circle of radius 21 cm, an arc subtends an angle of 72° at the centre. The length of the arc is

Detailed Solution: Question 15

We know that,
length of arc = Θ × radius

Hence, option B is correct.

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About this SSC CGL Practice Test

This test contains 15 MCQs on MCQ: Circles - 2 with detailed solutions for each question. It is part of the Quantitative Aptitude for SSC CGL course on EduRev, designed to align with the current SSC CGL syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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