Circles Class 10 MCQ with Answers – Maths

Circles Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test are covered in this Article. Circles Class 10 MCQ Test contains 25 questions. Answers to MCQs on Circles Class 10 MCQ with Answers Maths are available at the end of the last question. These MCQ have been made for Class 10 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.

Board	CBSE
Textbook	Maths (NCERT)
Class	Class 10
Chapter	Chapter 10 Circles
Category	MCQ Questions for Class 10 Maths with Answers

Circles Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

1. Figure showing tangent of a circle:

a) a
b) b
c) c
d) None

2. The tangent at any point of a circle is …………… to the radius through the point of contact.
a) Parallel
b) Perpendicular
c) Intersect
d) Angular

3. A chord with a zero secant is
a) Radius
b) Chord
c) Secant
d) Tangent

4. The no. of tangents drawn from an external point to a circle.
a) 1
b) 2
c) 3
d) 4

5. The no. of tangent to a circle passing through a point lying inside the circle.
a) 1
b) 2
c) 3
d) None

6. The no. of tangent to a circle passing through a point lying on the circle.
a) 1
b) 2
c) 3
d) 4

7. Length of the tangent is
a) From internal point to point of contact
b) From point of contact to mid point of chord
c) From external point to point of contact
d) From center to point of contact

8. If angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is:
a) 90º
b) 60º
c) 70º
d) 100º

9. A point which is at a distance of 10 cm from the center of a circle of radius 6 cm, the pair of tangents to the circle are drawn. find the area of the quadrilateral.
a) 36cm²
b) 48cm²
c) 56cm²
d) 60cm²

10. The two tangents are inclined at an angle 90° are drawn to a circle of radius 4 cm. Find the length of each tangent
a) 4cm
b) 5cm
c) 6cm
d) 7cm

Circles Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

11. Two circles with the centers O and O’ touching each other internally at A. Tangents TB and TA are drawn to the larger circle and tangents TA and TC are drawn to the smaller circle. Find TB: TC
a) 3:2
b) 2:3
c) 3:4
d) 1:1

12. The tangents drawn at the ends of a diameter of a circle are
a) perpendicular
b) parallel
c) Equal
d) Intersecting

13. The distance between two parallel tangents to a circle of radius 7 cm is
a) 5cm
b) 7cm
c) 10cm
d) 14cm

14. Find length of the chord.
a) 4cm
b) 6cm
c) 10cm
d) 12cm

15. Draw a circle, take a point outside it. And how many tangents can you draw to the circle through this point.
a) 1
b) 2
c) 3
d) 4

16. The ratio of the lengths of the two tangents from an external point to a circle are
a) 1:1
b) 1:2
c) 1:3
d) 1:4

17. A line ‘l’ intersecting the circle in two distinct points is
a) Chord
b) Tangent
c) Secant
d) Diameter

18. ∆ABC is an isosceles triangle. Find BC

a) 4cm
b) 5cm
c) 6cm
d) 7 cm

19. The tangent from an external point on a circle is
a) always makes 90˚ with the radius of the circle.
b) always >90˚ with the radius of the circle.
c) always <90˚ with the radius of the circle.
d) always makes 45˚ with the radius of circle

20. Find <TOP, where OP bisects < TPR

a) 30˚
b) 45˚
c) 60˚
d) 90˚

21. The line segment that joins two distinct points of a circle is
a) Secant
b) Tangent
c) Chord
d) Diameter

22. A chord that passes through the center of the circle is
a) Diameter
b) Radius
c) Secant
d) Chord

23. A circle is inscribed in a square of side 4cm. Find the angle subtended by the diagonals at the center of circle.
a) 60˚
b) 90˚
c) 110˚
d) None

24. Two parallel lines touch the circle at points A and B respectively. If area of the circle is 49πcm2, then AB is equal to
a) 5 cm
b) 8 cm
c) 14 cm
d) 25 cm

25. O is the center of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 80°, ∠BAT =?
a) 100°
b) 40°
c) 50°
d) 90°

Circles Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test – Correct Answers

1. Answer: C

Solution:  A line that intersects the circle at only one point is called a Tangent.

2. Answer: B

3. Answer: D

4. Answer: B

5. Answer: D

6. Answer: A

7. Answer: C

8. Answer: C
Solution: In a quad OPQR,
OP⊥ PQ and OR⊥ QR
<P +<Q +<R +<O= 360º
90º + <Q + 90º + 110º = 360º
<Q = 70º

9. Answer: B

Solution:
In ∆ OPR,
<P = 90˚ as PR is a tangent to a circle
OP = 6cm, OR = 10cm, PR =?
PR² = OR² – OP²
=100-36 =64
PR = 8cm
Ar quad POQR = 2(Ar of ∆ OPR)
= 2 × (1/2 ×OP × PR)
= 6 × 8
= 48cm²

10. Answer: A

Solution:
∆ OPR ≅∆ OQR (SSS congruency)
<ORP = <ORQ (CPCT)
IN ∆ OPR, OP⊥ PR
<ORP = 45˚, OP = 4cm
tan 45˚ = OP/PR ⇒   1= OP/PR
PR = OP =4cm

Circles Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

11. Answer: D

Solution:
The lengths of tangents drawn from an external point to a circle are equal.
In larger circle, TA = TB
In smaller circle, TA = TC
Therefore, TB = TC
TB/ TC = 1: 1

12. Answer: B

13. Answer: D

14. Answer: D

Solution:  PQ is a tangent to C2 at R and OR is its radius.
Therefore, OR ⊥ PQ
OR is the bisector of the chord PQ, as the perpendicular from the center bisects the chord.
Therefore, PR = RQ
In triangle ORP, OP = 10cm, OR = 10-2 =8cm, PR =?
OP² = OR² + PR²
PR² = OP² – OR² = 100 -64 = 36
PR = 6cm
PQ = PR + RQ = 6 + 6 = 12cm

15. Answer: B
Solution: There are exactly two tangents to a circle through a point lying outside the circle.

16. Answer: A
Solution: The lengths of the two tangents from an external point to a circle are equal.

17. Answer: C

18. Answer: C

Solution: AB = AC =5cm
The lengths of tangents drawn from an external point to a circle are equal.
Therefore, AP = AR = 2cm
QC = RC = AC – AR =5-2 = 3cm
BQ = PB = 3cm
BC = BQ + QC = 3+ 3 = 6cm

19. Answer: A

Solution:  The tangent at any point of a circle is perpendicular to the radius through the point of contact.

20. Answer: B

Solution:

OT = OR (Radii of the same circle)
OP = OP (Common)
Therefore, ∆ OTP ≅ ∆ ORP (RHS)
<TOP = <POR (CPCT)
In ∆ OTP,
< TOP + < TPO + < PTO = 180˚
< TOP = 180˚ – 90˚ -45˚ =45˚

Circles Class 10 MCQ with Answers – Maths Class 10 MCQ Online Test

21. Answer: C

22. Answer: A

23. Answer: B

Solution:  The diagonals of a square are equal and bisect each other at right angles.

24. Answer: C

Solution:
∴ πR² = 49π
⇒ R = 7 cm
∴ Distance between two parallel tangents = diameter = 2 × 7 = 14 cm.

25. Answer: B

Solution: ∠AOB = 80°
∠OAB = ∠OBA (∵ OA and OB are radii)
In ∆AOB,
∠AOB + ∠OAB + ∠OBA = 180°
⇒ 80° + x + x = 180°
⇒ 2x = 180° – 80°
⇒ 2x = 100°
⇒ x = 50°
Also, ∠OAB + ∠BAT = 90°
[TA is tangent at A]
⇒ 50° + <BAT = 90°
⇒ ∠BAT = 40˚

 

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