SSC CGL Circles MCQs with exam-oriented questions, detailed solutions, shortcut tricks and Tier-I & Tier-II practice for faster and more accurate preparation.
SSC CGL Circles MCQs
1. A tangent to a circle at point P is perpendicular to the radius drawn through P. If OP = 7 cm, where O is the centre, then the angle between OP and the tangent at P is
A) 45° B) 60°
C) 90° D) 180°
Correct Answer: C) 90°
Explanation:
The radius drawn to the point of contact of a tangent is always perpendicular to the tangent.
∴ ,∠OPT = 90°
2. From an external point P, a tangent PA is drawn to a circle with centre O. If OP = 13 cm and radius = 5 cm, find PA
A) 8 cm B) 10 cm
C) 12 cm D) 18 cm
Correct Answer: C) 12 cm
Explanation:
OA ⟂ PA
By Pythagoras theorem
PA² = OP² − OA²
= 13² − 5²
= 169 − 25
= 144
∴ PA = 12 cm
3. Two tangents PA and PB are drawn from an external point P to a circle. If PA = 9 cm, then PB is
A) 4.5 cm B) 9 cm
C) 18 cm D) Cannot be determined
Correct Answer: B) 9 cm
Explanation:
Tangents drawn from the same external point to a circle are equal.
PA = PB = 9 cm
4. The radius of a circle is 14 cm. Find its circumference. Take π = 22/7
A) 44 cm B) 66 cm
C) 88 cm D) 176 cm
Correct Answer: C) 88 cm
Explanation:
Circumference = 2πr
= 2 × 22/7 × 14
= 88 cm
5. The area of a circle is 154 cm². Find its radius. Take π = 22/7
A) 5 cm B) 6 cm
C) 7 cm D) 14 cm
Correct Answer: C) 7 cm
Explanation:
πr² = 154
(22/7)r² = 154
r² = 49
r = 7 cm
SSC CGL Circles MCQs
6. The radii of two circles are in the ratio 3 : 5. What is the ratio of their circumferences?
A) 3 : 5 B) 9 : 25
C) 5 : 3 D) 6 : 25
Correct Answer: A) 3 : 5
Explanation:
Circumference = 2πr
Circumference is directly proportional to radius
C₁ : C₂ = r₁ : r₂ = 3 : 5
7. The radii of two circles are in the ratio 2 : 3. Find the ratio of their areas
A) 2 : 3 B) 4 : 9
C) 3 : 2 D) 8 : 27
Correct Answer: B) 4 : 9
Explanation:
Area ∝ r²
A₁ : A₂ = 2² : 3²
= 4 : 9
8. The diameter of a circle is 28 cm. Its area is
A) 154 cm² B) 308 cm²
C) 616 cm² D) 1232 cm²
Correct Answer: C) 616 cm²
Explanation:
Radius = 28/2 = 14 cm
Area = πr²
= 22/7 × 14 × 14
= 616 cm²
9. The radius of a semicircle is 14 cm. Find its perimeter
A) 44 cm B) 58 cm
C) 72 cm D) 88 cm
Correct Answer: B) 72 cm
Explanation:
Perimeter of semicircle = πr + 2r
= 22/7 × 14 + 28
= 44 + 28
= 72 cm
10. A chord of a circle passes through the centre. Such a chord is called
A) Radius B) Tangent
C) Diameter D) Secant
Correct Answer: C) Diameter
Explanation:
A chord passing through the centre of a circle is called the diameter
A diameter is the longest chord of a circle
11. A perpendicular drawn from the centre of a circle to a chord
A) Doubles the chord B) Bisects the chord
C) Is parallel to the chord D) Is always equal to the chord
Correct Answer: B) Bisects the chord
Explanation:
The perpendicular from the centre of a circle to a chord bisects the chord.
If OM ⟂ AB, then
AM = MB
SSC CGL Circles MCQs
12. Two equal chords of a circle are
A) Equidistant from the centre B) Always diameters
C) Perpendicular to each other D) Parallel to each other
Correct Answer: A) Equidistant from the centre
Explanation:
Equal chords of the same circle are equidistant from the centre
Conversely, chords equidistant from the centre are equal
13. An arc of a circle subtends an angle of 80° at the circumference. What angle does the same arc subtend at the centre?
A) 40° B) 80°
C) 160° D) 240°
Correct Answer: C) 160°
Explanation:
Angle at centre = 2 × angle at circumference
= 2 × 80°
= 160°
14. An angle subtended by a diameter at any point on the circle is
A) 30° B) 45°
C) 60° D) 90°
Correct Answer: D) 90°
Explanation:
According to the theorem, the angle in a semicircle is always a right angle
Required angle = 90°
15. ABCD is a cyclic quadrilateral. If ∠A = 75°, find ∠C
A) 75° B) 90°
C) 105° D) 115°
Correct Answer: C) 105°
Explanation:
Opposite angles of a cyclic quadrilateral are supplementary
∠A + ∠C = 180°
75° + ∠C = 180°
∠C = 105°
SSC CGL Circles MCQs
16. In a cyclic quadrilateral, ∠A = 2x and ∠C = 3x. Find x
A) 30° B) 36°
C) 40° D) 45°
Correct Answer: B) 36°
Explanation:
Opposite angles are supplementary
2x + 3x = 180°
5x = 180°
x = 36°
SSC CGL Circles MCQs
17. The angle between a tangent and a chord through the point of contact is equal to
A) Angle at the centre B) Angle in the alternate segment
C) Double the angle in the alternate segment D) 90° always
Correct Answer: B) Angle in the alternate segment
Explanation:
By the tangent-chord theorem, the angle between a tangent and a chord equals the angle subtended by that chord in the alternate segment.
18. A tangent touches a circle at P. If OP is the radius, then
A) OP is parallel to tangent B) OP bisects tangent
C) OP is perpendicular to tangent D) OP is equal to tangent
Correct Answer: C) OP is perpendicular to the tangent
Explanation:
The radius drawn to the point of contact is perpendicular to the tangent.
OP ⟂ tangent.
19. From an external point P, two tangents PA and PB touch a circle with centre O. If ∠APB = 70°, find ∠AOB
- A) 70° B) 90° C) 110° D) 140°
Correct Answer: C) 110°
Explanation:
OA ⟂ PA and OB ⟂ PB
Thus, in quadrilateral OAPB
∠OAP = ∠OBP = 90°
∠AOB + ∠APB + 90° + 90° = 360°
∠AOB + 70° = 180°
∠AOB = 110°
20. A chord is 16 cm long, and its distance from the centre is 6 cm. Find the radius of the circle
A) 8 cm B) 10 cm
C) 12 cm D) 14 cm
Correct Answer: B) 10 cm
Explanation:
Perpendicular from centre bisects the chord
Half chord = 16/2 = 8 cm
Using Pythagoras
r² = 8² + 6²
= 64 + 36
= 100
r = 10 cm
SSC CGL Circles MCQs
21. A circle has a radius of 13 cm. A chord is at a distance of 5 cm from the centre. Find the chord length
A) 10 cm B) 12 cm
C) 24 cm D) 26 cm
Correct Answer: C) 24 cm
Explanation:
Half chord = √(r² − d²)
= √(13² − 5²)
= √(169 − 25)
= √144
= 12 cm
∴ chord = 2 × 12 = 24 cm
22. The maximum possible length of a chord of a circle whose radius is 17 cm is
A) 8.5 cm B) 17 cm
C) 34 cm D) 289 cm
Correct Answer: C) 34 cm
Explanation:
The diameter is the longest chord
Diameter = 2r
= 2 × 17
= 34 cm
23. A chord of length 24 cm belongs to a circle of radius 13 cm. Its distance from the centre is
A) 5 cm B) 7 cm
C) 10 cm D) 12 cm
Correct Answer: A) 5 cm
Explanation:
Half chord = 12 cm.
d² = r² − (half chord)²
= 13² − 12²
= 169 − 144
= 25
∴ d = 5 cm.
24. Two concentric circles have radii 14 cm and 7 cm. Find the area of the region between them. Take π = 22/7
A) 308 cm² B) 462 cm²
C) 616 cm² D) 770 cm²
Correct Answer: C) 462 cm²
Explanation:
Area of ring = π(R² − r²)
= 22/7 × (14² − 7²)
= 22/7 × (196 − 49)
= 22/7 × 147
= 462 cm²
SSC CGL Circles MCQs
25. The area of a sector of angle 90° in a circle of radius 14 cm is
A) 77 cm² B) 154 cm²
C) 308 cm² D) 616 cm²
Correct Answer: B) 154 cm²
Explanation:
Area of sector = θ/360 × πr²
= 90/360 × 22/7 × 14²
= 1/4 × 616
= 154 cm²
26. Find the length of an arc subtending 90° at the centre of a circle of radius 14 cm.
A) 11 cm B) 22 cm
C) 44 cm D) 88 cm
Correct Answer: B) 22 cm
Explanation:
Arc length = θ/360 × 2πr
= 90/360 × 2 × 22/7 × 14
= 1/4 × 88
= 22 cm
SSC CGL Circles MCQs
27. A wheel has a radius of 35 cm. How much distance does it cover in 20 revolutions? Take π = 22/7
A) 22 m B) 44 m
C) 66 m D) 88 m
Correct Answer: B) 44 m
Explanation:
Distance in one revolution = circumference
= 2πr
= 2 × 22/7 × 35
= 220 cm.
For 20 revolutions
220 × 20 = 4400 cm
= 44 m
28. A circular wheel of diameter 70 cm travels 220 m. How many revolutions does it make? Take π = 22/7
A) 50 B) 75
C) 100 D) 125
Correct Answer: C) 100
Explanation:
Circumference = πd
= 22/7 × 70
= 220 cm.
Distance = 220 m = 22,000 cm.
Number of revolutions = 22,000/220
= 100
29. Two circles touch externally. The distance between their centers is 20 cm, and their radii are 8 cm and 12 cm. The circles
A) Do not touch B) Touch externally
C) Touch internally D) Intersect at two points
Correct Answer: B) Touch externally
Explanation:
For external contact
Distance between centers = sum of radii.
8 + 12 = 20 cm.
Since the given distance is 20 cm, the circles touch externally
30. Two circles have radii 15 cm and 7 cm. Their centers are 8 cm apart. How do they relate to each other?
A) Touch externally B) Intersect at two points
C) Touch internally D) Do not meet
Correct Answer: C) Touch internally
Explanation:
For internal contact
Distance between centers = difference between radii.
15 − 7 = 8 cm.
Since the distance between the centers is 8 cm, the smaller circle touches the larger circle internally.
SSC CGL Circles MCQs
SSC CGL Quantitative Aptitude Topics
- Number System
- Decimals
- Fractions
- Percentages
- Ratio & proportion
- Square roots
- Averages
- Interest (simple & compound)
- Profit & loss
- Discount
- Partnerships
- Mixture & Alligation
- Time & speed & distance
- Time & work
- Advanced math includes basic algebraic identities
- Elementary surds
- Linear equations
- Triangles
- Circles
- Regular polygons, right prisms, cones, cylinders, spheres
- Trigonometry
YOUTUBE
If you are interested in reading stories, CLICK HERE
