Welcome to your Circles MCQs Mock Test of 10th Class Mathematics

1.
Q1. In the figure below, PQ is a chord of a circle and PT is the tangent at P such that ∠QPT = 60°. Then ∠PRQ is equal to

2.
Q2. A circle has a number of tangents equal to

3.
Q3. In the below figure, if ∠AOB = 125°, then ∠COD is equal to

4.
Q4. A tangent intersects the circle at:

5.
Q5. In the figure, PQL and PRM are tangents to the circle with centre O at the points Q and R, respectively and S is a point on the circle such that ∠SQL = 50° and ∠SRM = 60°. Then ∠QSR is equal to

6.
Q6. A circle can have _____parallel tangents at a single time.

7.
Q7. Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. The radius of the inner circle will be

8.
Q8. If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is:

9.
Q9. The distance between two parallel tangents of a circle is 18 cm, then the radius of the circle is

10.
Q10. The length of the tangent from an external point A on a circle with centre O is

11.
Q11. 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

12.
Q12. If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

13.
Q13. The area of a circle whose circumference is 22 cm, is

14.
Q14. The area of a circle is 154 cm². Its diameter is

15.
Q15. The area of a quadrant of a circle whose circumference is 22 cm, is

16.
Q16. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 7 m long rope. The area of that part of the field in which the horse can graze, is

17.
Q17. The area of the circle whose diameter is 21 cm is

18.
Q18. The area of the sector of a circle with radius 6 cm and of angle 60° is

19.
Q19. The area of the circle that can be inscribed in a square of side 6 cm is :

20.
Q20. The area of the circle is 154 cm². The radius of the circle is

21.
Q21. If angle of sector is 60°, radius is 3.5 cm then length of the arc is

22.
Q22. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is :

23.
Q23. The area of the square that can be inscribed in a circle of radius 8 cm is

24.
Q24. If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R, then :

25.
Q25. If the circumference of a circle and the perimeter of a square are equal then :

26.
Q26. Area of the largest triangle that can be inscribed in a semi-circle of radius ‘‘ units is :

27.
Q27. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be :

28.
Q28. 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:

29.
Q29. If a parallelogram circumscribes a circle, then it is a:

30.
Q30. 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:

31.
Q31. If angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is

32.
Q32. A line intersecting a circle in two points is called a _______.

33.
Q33. In the figure below, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is

34.
Q34. 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

35.
Q35. The tangent to a circle is ___________ to the radius through the point of contact.

36.
Q36. The area of the shaded region in Fig., where arcs drawn with centres P, Q, Rand S intersect in pairs at mid-points A, B, C and D of the sides PQ, QR, RS and SP, respectively of a square PQRS, is:

37.
Q37. If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then

38.
Q38. Area of a sector of central angle 120° of a circle is 3π cm2. Then the length of the corresponding arc of this sector is:

39.
Q39. If the circumference of a circle and the perimeter of a square are equal, then

40.
Q40. A round table cover has six equal designs as shown in the figure. If the radius of thecover is 28 cm, then the cost of making the design at the rate of Rs. 0.35 per cm2 is:

41.
Q41. Area of the largest triangle that can be inscribed in a semi-circle of radius r units, in square units is:

42.
Q42. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is:

43.
Q43. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be

44.
Q44. The area of the circle that can be inscribed in a square of side 6 cm is

45.
Q45. The area of the square that can be inscribed in a circle of radius 8 cm is

46.
Q46. The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is

47.
Q47. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm respectively, is

48.
Q48. If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then

49.
Q49. The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/h?

50.
Q50. A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20m × 16m, then the area of the field in which the cow can graze is: