Class 10 Maths Chapter 9 MCQs – Chords of a Circle (FBISE)

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Description: Practice Class 10 Maths Chapter 9 MCQs on Chords of a Circle. These multiple choice questions cover circle theorems and are designed according to FBISE exam pattern.

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1. A chord is a line segment joining:

A) Center to circumference
B) Two points on the circle
C) Radius to tangent
D) Diameter to radius

2. The longest chord of a circle is:

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

3. A perpendicular drawn from center to a chord:

A) Is unequal
B) Is tangent
C) Bisects the chord
D) Extends outside

4. Equal chords of a circle are:

A) Unequal in distance
B) Parallel
C) Intersecting
D) Equidistant from center

5. Chords equidistant from center are:

A) Unequal
B) Equal
C) Parallel
D) Tangent

6. If two chords intersect inside a circle, then:

A) Product of segments are equal
B) Sum is equal
C) Difference is equal
D) Angles are equal

7. If two chords AB and CD intersect at P, then:

A) AP + PB = CP + PD
B) AP – PB = CP – PD
C) $AP \times PB = CP \times PD$
D) AP = PB

8. If perpendicular from center to chord is zero, chord is:

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

9. If two chords are equal, their distances from center are:

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

10. A diameter divides the circle into:

A) Two unequal parts
B) Two equal parts
C) Three parts
D) Four parts

11. The perpendicular from center to chord is:

A) Longer than chord
B) Equal to radius
C) Shortest distance
D) Infinite

12. If two chords are unequal, then their distances from center are:

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

13. The line joining center to midpoint of chord is:

A) Parallel
B) Tangent
C) Arc
D) Perpendicular

14. If a line passes through center and bisects a chord, it is:

A) Tangent
B) Perpendicular to chord
C) Arc
D) Radius

15. Equal chords subtend equal:

A) Lengths
B) Radii
C) Angles at center
D) Areas

16. If chords subtend equal angles at center, they are:

A) Equal
B) Unequal
C) Tangent
D) Diameter

17. Chords are always inside the:

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

18. If two chords intersect inside a circle, then the product of their segments is:

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

19. If chords AB and CD intersect at P, then:

A) $AP \times PB = CP \times PD$
B) $AP + PB = CP + PD$
C) $AP = CP$
D) $PB = PD$

20. If one chord is a diameter, then angle in semicircle is:

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

21. If a perpendicular from center bisects a chord, then:

A) Chord is diameter
B) It passes through midpoint
C) It is tangent
D) It is arc

22. Equal chords subtend equal angles at:

A) Center
B) Circumference
C) Tangent
D) Radius

23. If two chords subtend equal angles at center, then:

A) They intersect
B) They are perpendicular
C) They are equal
D) They are tangent

24. If two chords are at equal distance from center, then:

A) They are unequal
B) They are equal
C) They are parallel
D) They are perpendicular

25. If a line from center is perpendicular to chord, it:

A) Doubles chord
B) Extends chord
C) Touches circle
D) Bisects chord

26. If chord length increases, distance from center:

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

27. The midpoint of a chord lies on:

A) Circle
B) Arc
C) Perpendicular from center
D) Tangent

28. If two chords intersect outside the circle, the theorem used is:

A) Pythagoras theorem
B) Secant theorem
C) Cosine rule
D) Sine rule

29. If $AP = 3, PB = 4$ , then product is:

A) 12
B) 7
C) 1
D) 16

30. If $AP \times PB = CP \times PD$ and one product is 20, the other is:

A) 10
B) 15
C) 25
D) 20

31. Diameter is perpendicular to tangent at:

A) Center
B) Outside point
C) Point of contact
D) Midpoint

32. If chord passes through center, it becomes:

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

33. The distance from center to chord is measured along:

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

34. If two chords intersect, number of segments formed are:

A) 2
B) 3
C) 5
D) 4

35. If a chord is far from the center, its length is:

A) Smaller
B) Larger
C) Equal
D) Infinite

36. If a chord is near the center, its length is:

A) Small
B) Zero
C) Larger
D) Negative

37. If two chords are equal, their perpendicular distances from center are:

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

38. If distance from center decreases, chord length:

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

39. The diameter is always:

A) Largest chord
B) Smallest chord
C) Tangent
D) Arc

40. If two chords intersect and one segment is zero, then:

A) Circle disappears
B) Chords are equal
C) Intersection is on circumference
D) No solution

41. If $AP = 2, PB = 6$ , then product is:

A) 8
B) 12
C) 4
D) 16

42. If $AP \times PB = 12$ , and $CP = 3$ , then $PD =$

A) 2
B) 3
C) 6
D) 4

43. If chords intersect at center, they become:

A) Diameters
B) Tangents
C) Arcs
D) Radii

44. If a chord is equal to radius, triangle formed is:

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

45. The number of diameters in a circle is:

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

46. If midpoint of chord is known, perpendicular from center:

A) Is unequal
B) Is tangent
C) Extends outside
D) Passes through midpoint

47. If chord length is maximum, distance from center is:

A) Zero
B) Maximum
C) Infinite
D) Negative

48. If distance from center is maximum, chord length is:

A) Maximum
B) Equal
C) Minimum
D) Infinite

49. If a chord passes through center, it divides circle into:

A) Unequal parts
B) Equal parts
C) Three parts
D) Four parts

50. Chords are used to study:

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

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