Class 10 Maths Chapter 10 MCQs – Tangents to a Circle (FBISE)

Description: Practice Class 10 Maths Chapter 10 MCQs on Tangents to a Circle. These questions are based on important theorems and FBISE exam pattern.

1. A tangent to a circle touches it at:

A) Two points
B) One point
C) Three points
D) No point

2. The point where tangent touches the circle is called:

A) Point of contact
B) Center
C) Radius
D) Arc

3. A tangent is perpendicular to radius at:

A) Center
B) Diameter
C) Point of contact
D) Arc

4. Number of tangents from a point on the circle is:

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

5. Number of tangents from a point outside the circle is:

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

6. Lengths of tangents drawn from an external point are:

A) Equal
B) Unequal
C) Zero
D) Infinite

7. If PA and PB are tangents from point P, then:

A) PA > PB
B) PA < PB
C) PA = PB
D) PA + PB = 0

8. The angle between tangent and radius at point of contact is:

A) 45^\circ
B) 90^\circ
C) 60^\circ
D) 30^\circ

9. If a line cuts a circle at two points, it is called:

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

10. A line that touches the circle at exactly one point is:

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

11. If radius is drawn to point of contact, it is:

A) Parallel
B) Inclined
C) Perpendicular to tangent
D) Tangent

12. From a point inside the circle, number of tangents is:

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

13. Tangent is always:

A) Outside the circle
B) Inside the circle
C) Through center
D) Diameter

14. If tangent length is zero, point lies:

A) Outside circle
B) Inside circle
C) At center
D) On the circle

15. Tangent segment is drawn from:

A) Center
B) Radius
C) External point
D) Arc

16. The distance from center to tangent is equal to:

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

17. If a line is perpendicular to radius at its endpoint on circle, it is:

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

18. If tangents are drawn from an external point, they are:

A) Equal in length
B) Unequal
C) Parallel
D) Perpendicular

19. If PA and PB are tangents from P, then triangle PAB is:

A) Scalene
B) Right angled
C) Isosceles
D) Equilateral

20. If length of tangent from point P is 5 cm, then both tangents are:

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

21. If distance of point from center is equal to radius, then tangent length is:

A) Maximum
B) Equal to radius
C) Infinite
D) Zero

22. If distance from center is less than radius, tangents are:

A) Not possible
B) Equal
C) One
D) Infinite

23. If distance from center is greater than radius, number of tangents is:

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

24. The tangent length formula is:

A) PT = r^2 - d^2
B) PT = \sqrt{d^2 - r^2}
C) PT = d^2 + r^2
D) PT = d - r

25. If d = 13 cm and r = 5 cm, tangent length is:

A) 12 cm
B) 8 cm
C) 18 cm
D) 10 cm

26. If tangent length is zero, point lies:

A) Outside circle
B) Inside circle
C) At center
D) On circle

27. If two tangents are drawn, angle between them depends on:

A) Radius only
B) Diameter
C) Position of external point
D) Arc

28. The line joining external point to center bisects:

A) Radius
B) Angle between tangents
C) Diameter
D) Arc

29. If angle between two tangents is 60^\circ, then angle at center is:

A) 120^\circ
B) 60^\circ
C) 90^\circ
D) 180^\circ

30. If angle at center is 90^\circ, angle between tangents is:

A) 180^\circ
B) 45^\circ
C) 60^\circ
D) 90^\circ

31. Tangent at any point of circle is:

A) Parallel to radius
B) Inclined
C) Perpendicular to radius
D) Equal to radius

32. If tangent length increases, external point moves:

A) Towards circle
B) Away from circle
C) On circle
D) Inside circle

33. The distance between center and tangent is always:

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

34. If two tangents meet, they form:

A) Circle
B) Line
C) Arc
D) Angle

35. If d = 10 cm and r = 6 cm, tangent length is:

A) 8 cm
B) 4 cm
C) 16 cm
D) 6 cm

36. If a point lies inside a circle, tangents drawn are:

A) One
B) Two
C) None
D) Infinite

37. If a point lies on the circle, number of tangents is:

A) Two
B) One
C) None
D) Infinite

38. If a point lies outside the circle, number of tangents is:

A) One
B) None
C) Infinite
D) Two

39. If PT = 5 cm, then both tangent segments from point P are:

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

40. If radius is 5 cm and tangent length is 12 cm, distance from center is:

A) 17 cm
B) 10 cm
C) 13 cm
D) 7 cm

41. If angle between tangents is 90^\circ, angle at center is:

A) 45^\circ
B) 90^\circ
C) 180^\circ
D) 60^\circ

42. If angle at center is 120^\circ, angle between tangents is:

A) 120^\circ
B) 30^\circ
C) 90^\circ
D) 60^\circ

43. The tangent is always:

A) Perpendicular to radius
B) Parallel to radius
C) Equal to radius
D) Greater than radius

44. If two tangents are equal, triangle formed is:

A) Scalene
B) Right angled
C) Isosceles
D) Equilateral

45. The center of circle lies on:

A) Tangent
B) Perpendicular bisector of chord
C) Arc
D) Radius only

46. If tangent length increases, distance from center:

A) Decreases
B) Remains same
C) Becomes zero
D) Increases

47. If distance from center equals radius, tangent length is:

A) 0
B) 1
C) r
D) Infinite

48. If two tangents are perpendicular, angle at center is:

A) 45^\circ
B) 60^\circ
C) 90^\circ
D) 120^\circ

49. If radius is doubled, tangent length:

A) Decreases
B) Changes accordingly
C) Remains same
D) Becomes zero

50. Tangents are used to study:

A) Circle geometry
B) Algebra
C) Statistics
D) Arithmetic

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