MCQs for** Class 10 Maths Chapter 10 Circles**: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

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# Class 10 MCQ Maths Chapter 10 Circles

1. A circle has a number of tangents equal to

(a)0

(b)1

(c)2

(d)Infinite

Answer: (d)Infinite

2. The length of tangent from an external point P on a circle with centre O is

(a) always greater than OP

(b) equal to OP

(c) always less than OP

(d) information insufficient

Answer: (c) always less than OP

3. If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is

(a) 3 cm

(b) 6 cm

(c) 9 cm

(d) 1 cm

Answer: (b) 6 cm

4. The distance between two parallel tangents of acircle of radius 4 cm is

(a) 2 cm

(b) 4 cm

(c) 6 cm

(d) 8 cm

Answer: (d) 8 cm

5. A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of its tangent is

(a) 5 cm

(b) 9 cm

(c) 15 cm

(d) 23 cm

Answer: (c) 15 cm

6. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is

(a) 60 cm2

(b) 65 cm2

(c) 30 cm2

(d) 32.5 cm2

Answer: (a) 60 cm2

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7. In the given figure, PA and PB are tangents from P to a circle with centre O. If ∠AOB = 130°, then find ∠APB.

(a) 40°

(b) 55°

(c) 50°

(d) 60°

Answer: (c) 50°

8. A tangent intersects the circle at:

(a)One point

(b)Two distinct point

(c)At the circle

(d)None of the above

Answer: (a)One point

9. If angle between two tangents drawn from a point P to a circle of radius ‘a’and centre ‘O’ is 90°, then OP =

(a) 2a√2

(b) a√2

(c) a/√2

(d) 5a√2

Answer: (b) a√2

10. From a point P which is at a distance of 13 cm from the point O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is

(a) 60 cm²

(b) 65 cm²

(c) 30 cm²

(d) 32.5 cm²

Answer: (a) 60 cm²

11. A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of its tangent is

(a) 5 cm

(b) 9 cm

(c) 15 cm

(d) 23 cm

Answer: (c) 15 cm

12. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such ∠POR = 120°, then ∠OPQ is

(a) 45°

(b) 30°

(c) 60°

(d) 35°

Answer: (b) 30°

13. In the given figure, PT is a tangent to a circle whose centre is O. If PT = 12 cm and PO = 13 cm then find teh radius of the circle.

(a) 5 cm

(b) 4 cm

(c) 6 cm

(d) 4.5 cm

Answer: (b) 4 cm

14. A circle can have _____parallel tangents at a single time.

(a)One

(b)Two

(c)Three

(d)Four

Answer: (b)Two

15. The length of tangent from an external point on a circle is

(a) always greater than the radius of the circle.

(b) always less than the radius of the circle.

(c) may or may not be greater than the radius of circle

(d) None of these.

Answer: (c) may or may not be greater than the radius of circle

16. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 8 cm

Answer: (d) 8 cm

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17. The length of tangents drawn from an external point to the circle

(a) are equal

(b) are not equal

(c) sometimes are equal

(d) are not defined

Answer: (a) are equal

18. Number of tangents drawn at a point of the , circle is/are

(a) one

(b) two

(c) none

(d) infinite

Answer: (a) one

19. A line that intersects a circle in exactly one point is called a

(a) Diameter

(b) Tangent

(c) Radius

(d) Chord

Answer: (b) Tangent

20. In the given figure, PT is a tangent to the circle and O is its centre. Find OP.

(a) 16 cm

(b) 15 cm

(c) 18 cm

(d) 17 cm

Answer: (c) 18 cm

21. If the 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)50º

(c)70º

(c)40º

Answer: (c)70º

22. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 8 cm

Answer: (d) 8 cm

23. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm the length of each tangent is equal to

(a) 3/2√3 cm

(b) 6 cm

(c) 3 cm

(d) 3√3 cm

Answer: (d) 3√3 cm

24. The tangents drawn at the extremities of the diameter of a circle are

(a) perpendicular

(b) parallel

(c) equal

(d) none of these

Answer: (b) parallel

25. Tangents from an external point to a circle are

(a) equal

(b) not equal

(c) parallel

(d) perpendicular

Answer: (a) equal

26. A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x =

(a) 20 cm

(b) 24 cm

(c) 18 cm

(d) 12 cm

Answer: (b) 24 cm

27. The length of the tangent from an external point A on a circle with centre O is

(a)always greater than OA

(b)equal to OA

(c)always less than OA

(d)Cannot be estimated

Answer: (c)always less than OA

28. If d_{1}, d_{2} (d_{2} > d_{1}) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, then

(a) d_{2}^{2} = c^{2} + d_{1}^{2}

(b) d_{2}^{2} = c^{2} – d_{1}^{2}

(c) d_{1}^{2} = c^{2} + d_{2}^{2}

(d) d_{1}^{2} = c^{2} – d_{2}^{2}

Answer:(a) d_{2}^{2} = c^{2} + d_{1}^{2}

29. The length of a tangent drawn from a point at a distance of 10 cm of circle is 8 cm. The radius of the circle is

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 7 cm

Answer: (c) 6 cm

30.A line through point of contact and passing through centre of circle is known as

(a) tangent

(b) chord

(c) normal

(d) segment

Answer: (c) normal

31. From a point X, the length of the tangent to a circle is 20 cm and the distance of X from the centre is 25 cm. The radius of the circle is

(a) 10 cm

(b) 5√41 cm

(c) 15 cm

(d) 20 cm

Answer: (c) 15 cm

32. AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to

(a)65°

(b)60°

(c)50°

(d)40°

Answer: (c)50°

33.If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is:

(a) 60°

(b) 120°

(c) 80°

(d) 100°

Answer: (a) 60°

34. C (O, r_{1}) and C(O, r_{2}) are two concentric circles with r_{1} > r_{2} AB is a chord of C(O, r_{1}) touching C(O, r,_{2}) at C then

(a) AB = r_{1}

(b) AB = r_{2}

(c) AC = BC

(d) AB = r_{1} + r_{2}

Answer: (c) AC = BC

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35. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°, then ∠OPQ is

(a) 60°

(b) 45°

(c) 30°

(d) 90°

Answer: (c) 30°

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36.If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

(a)60°

(b)70°

(c)80°

(d)90°

Answer: (b)70°

37. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to

(a) 2√3 cm

(b) 6√3 cm

(c) 3√3 cm

(d) 3 cm

Answer: (c) 3√3 cm

38. Two parallel lines touch the circle at points A and B respectively. If area of the circle is 25 n cm^{2}, then AB is equal to

(a) 5 cm

(b) 8 cm

(c) 10 cm

(d) 25 cm

Answer: (c) 10 cm

39. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ = 12 cm. Length PQ is

(a) 12 cm

(b) 13 cm

(c) 8.5 cm

(d) √119 cm

Answer: (d) √119 cm

40.The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:

(a)3cm

(b)5cm

(c)7cm

(d)10cm

Answer: (a)3cm

41. Two circle touch each other externally at C and AB is a common tangent to the circles. Then, ∠ACB =

(a) 60°

(b) 45°

(c) 30°

(d) 90°

Answer: (d) 90°

42. If a parallelogram circumscribes a circle, then it is a:

(a)Square

(b)Rectangle

(c)Rhombus

(d)None of the above

Answer: (c)Rhombus

43. Number of tangents, that can be drawn to a circle, parallel to a given chord is

(a) 3

(b) Zero

(c) Infinite

(d) 2

Answer: (d) 2

44. Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is:

(a)8

(b)10

(c)12

(d)18

Answer: (a)8

45. The distance between two parallel tangents to a circle of radius 5 cm is

(a) 5cm

(b) 8cm

(c) 10cm

(d) 9cm

Answer: (c) 10cm

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46. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

(a) 7 cm

(b) 12 cm

(c) 15 cm

(d) 24.5 cm.

Answer: (a) 7 cm

47. A tangent to a circle is a line that intersects the circle in

(a) Exactly one point

(b) 2 points

(c) 3 points

(d) 4 points

Answer: (a) Exactly one point

48. AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to

(a) 4 cm

(b) 2 cm

(c) 2√3 cm

(d) 4√3 cm

Answer: (c) 2√3 cm

49. From a point X, the length of the tangent to a circle is 20 cm and the distance of X from the centre is 25 cm. The radius of the circle is

(a) 10 cm

(b) 5√41 cm

(c) 15 cm

(d) 20 cm

Answer: (c) 15 cm

50. The length of tangents drawn from an external point to the circle

(a) are equal

(b) are not equal

(c) sometimes are equal

(d) are not defined

Answer: (a) are equal

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