SSC CAPFS and DP - circle geometry - chords tangents angles subtended by chords, common tangents to circles Online Test (MCQ Quiz)

1. What is the definition of a chord in a circle?

A) A line segment connecting the center to a point on the circumference. B) A line segment whose endpoints both lie on the circle. C) A line segment passing through the center and touching the circumference at two points. D) A line that intersects the circle at exactly one point.

2. A tangent to a circle is a line that:

A) Intersects the circle at two distinct points. B) Passes through the center of the circle. C) Intersects the circle at exactly one point. D) Is a chord of the circle.

3. What is the angle between a tangent and the radius at the point of contact?

A) 0 degrees B) 45 degrees C) 90 degrees D) 180 degrees

4. If a chord passes through the center of a circle, it is called a:

A) Secant B) Radius C) Tangent D) Diameter

5. The angle subtended by a diameter at any point on the circumference is:

A) 45 degrees B) 90 degrees C) 135 degrees D) 180 degrees

6. Angles subtended by the same arc at the circumference are:

A) Always equal B) Always supplementary C) Always complementary D) Always double each other

7. If two circles touch each other externally, the number of common tangents is:

A) 1 B) 2 C) 3 D) 4

8. If two circles touch each other internally, the number of common tangents is:

A) 1 B) 2 C) 3 D) 4

9. If two circles are completely separate (do not intersect), the number of common tangents is:

A) 1 B) 2 C) 3 D) 4

10. If two circles intersect at two distinct points, the number of common tangents is:

A) 0 B) 1 C) 2 D) 3

11. The angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the:

A) Center B) Circumference C) Diameter D) Chord

12. A line segment joining the center of a circle to any point on its circumference is called a:

A) Chord B) Diameter C) Radius D) Secant

13. What is the longest possible chord in a circle?

A) Radius B) Diameter C) Tangent D) Secant

14. A line that intersects a circle at two points is called a:

A) Tangent B) Chord C) Secant D) Radius

15. If a chord is perpendicular to a diameter, the diameter:

A) Bisects the chord B) Bisects the arc subtended by the chord C) Both A and B D) Neither A nor B

16. Two parallel tangents to a circle are always:

A) Equidistant from the center B) At the ends of a diameter C) Both A and B D) Neither A nor B

17. The distance between the centers of two circles is 13 cm and their radii are 8 cm and 3 cm. What type of tangents do they have?

A) No common tangents B) One common tangent C) Two common tangents D) Three common tangents

18. Two circles have radii 5 cm and 2 cm. If the distance between their centers is 10 cm, how many common tangents can be drawn?

A) 1 B) 2 C) 3 D) 4

19. If the distance between the centers of two circles is equal to the sum of their radii, they touch:

A) Internally B) Externally C) Do not touch D) One inside the other

20. If the distance between the centers of two circles is equal to the difference of their radii, they touch:

A) Externally B) Internally C) Do not touch D) Are concentric

21. Let a chord AB of a circle be at a distance of 5 cm from the center. If the radius of the circle is 13 cm, find the length of the chord AB.

A) 10 cm B) 20 cm C) 24 cm D) 26 cm

22. In a circle, the angle subtended by an arc at the center is 120 degrees. The angle subtended by the same arc at any point on the circumference is:

A) 30 degrees B) 60 degrees C) 120 degrees D) 240 degrees

23. If two chords of a circle are equal in length, then they are:

A) Parallel B) Perpendicular C) Equidistant from the center D) Not necessarily equidistant from the center

24. The angle in a semicircle is:

A) Acute B) Right C) Obtuse D) Straight

25. Consider two circles with radii R and r (R > r). If the distance between their centers is d. For external common tangents to exist, which condition must be met?

A) d > R + r B) d = R + r C) d < R + r D) d = R - r

26. Consider two circles with radii R and r (R > r). If the distance between their centers is d. For internal common tangents to exist, which condition must be met?

A) d > R + r B) d = R + r C) d < R + r D) d = R - r

27. If two circles touch externally, the number of direct common tangents is:

A) 0 B) 1 C) 2 D) 3

28. If two circles touch internally, the number of direct common tangents is:

A) 0 B) 1 C) 2 D) 3

29. A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center.

A) 5 cm B) 6 cm C) 8 cm D) 10 cm

30. If two concentric circles have radii 7 cm and 3 cm, how many common tangents can be drawn?

A) 0 B) 1 C) 2 D) 4

31. What is the relationship between the angle subtended by an arc at the center and the angle subtended by it at the circumference?

A) Angle at center is half the angle at circumference. B) Angle at center is equal to the angle at circumference. C) Angle at center is double the angle at circumference. D) No fixed relationship.

32. Two circles of radii 10 cm and 6 cm are 20 cm apart. How many common tangents can be drawn?

A) 1 B) 2 C) 3 D) 4

33. If a chord subtends an angle of 60 degrees at the circumference, what is the angle subtended by it at the center?

A) 30 degrees B) 60 degrees C) 90 degrees D) 120 degrees

34. In a circle, if two arcs are equal, then the corresponding chords are:

A) Parallel B) Perpendicular C) Equal D) Half the length

35. A tangent is drawn to a circle of radius 5 cm. What is the distance from the center to the point of contact?

A) 0 cm B) 2.5 cm C) 5 cm D) 10 cm

36. If a circle is inscribed in a square, what is the relationship between the diameter of the circle and the side of the square?

A) Diameter is half the side B) Diameter is equal to the side C) Diameter is double the side D) No fixed relationship

37. If two circles touch externally at a point P, and AB is a common tangent, then angle APB is:

A) 45 degrees B) 60 degrees C) 90 degrees D) 180 degrees

38. Consider a circle with center O and radius r. If a point P is outside the circle, and PA and PB are tangents to the circle at points A and B respectively, then:

A) OA is perpendicular to PA B) OP bisects angle APB C) OP bisects angle AOB D) All of the above

39. If two circles intersect such that the distance between their centers is equal to the difference of their radii, they touch:

A) Externally B) Internally C) At two points D) Concurrently

40. A chord is 12 cm long and its distance from the center is 8 cm. What is the radius of the circle?

A) 8 cm B) 10 cm C) 12 cm D) 20 cm

41. If a line segment connects two points on a circle, it is a:

A) Tangent B) Secant C) Chord D) Radius

42. What is the maximum number of common tangents that can be drawn to two circles of different radii that intersect each other?

A) 0 B) 1 C) 2 D) 3

43. If a chord AB subtends an angle of 30 degrees at the circumference in the major segment, what is the angle subtended by the chord AB at the center?

A) 15 degrees B) 30 degrees C) 60 degrees D) 135 degrees

44. When two circles are tangent externally, the distance between their centers is:

A) The sum of their radii B) The difference of their radii C) Zero D) Greater than the sum of their radii

45. The angle subtended by a minor arc at the center is always:

A) Acute B) Right C) Obtuse D) Reflex

46. If a chord is equidistant from the center as another chord, then the lengths of the two chords are:

A) Half of each other B) Double of each other C) Equal D) Unrelated

47. If two tangents are drawn from an external point to a circle, they are:

A) Perpendicular to each other B) Equal in length C) Parallel to each other D) Half the length of the radius

48. Consider two circles with radii 6 cm and 4 cm. If they touch internally, what is the distance between their centers?

A) 2 cm B) 10 cm C) 24 cm D) 1 cm

49. A chord subtends an angle of 180 degrees at the center. This chord is a:

A) Radius B) Diameter C) Tangent D) Secant

circle geometry - chords tangents angles subtended by chords, common tangents to circles - Online Test

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