Revise smartly with Class 9 Maths Chapter 9 – Circles! Solve MCQs to test your understanding of properties like chords, angles, and cyclic quadrilaterals, and tackle fill-in-the-blanks that focus on key facts. With answers included, this practice set helps you gain confidence before exams.
Class 9th Maths Important MCQs with Answers from Chapter 9 – Circles
Question 1. Equal chords of a circle subtend equal ___ at the centre.
a) Sides
b) Radii
c) Angles
d) Distances
Answer:
c) Angles – Theorem 9.1 states equal chords subtend equal angles at the centre.
Question 2. If two chords of a circle subtend equal angles at the centre, then the chords are ___.
a) Unequal
b) Equal
c) Parallel
d) Perpendicular
Answer:
b) Equal – Converse of Theorem 9.1.
Question 3. The perpendicular from the centre of a circle to a chord always ___ the chord.
a) Bisects
b) Doubles
c) Triples
d) Shortens
Answer:
a) Bisects – Theorem 9.3.
Question 4. If a line from the centre bisects a chord, it is always ___ to the chord.
a) Parallel
b) Perpendicular
c) Equal
d) Tangent
Answer:
b) Perpendicular – Converse of Theorem 9.3.
Question 5. Equal chords of a circle are always equidistant from the ___.
a) Diameter
b) Centre
c) Circumference
d) Tangent
Answer:
b) Centre – Theorem 9.5.
Question 6. Chords equidistant from the centre of a circle are always ___ in length.
a) Unequal
b) Equal
c) Smaller
d) Longer
Answer:
b) Equal – Theorem 9.6.
Question 7. The angle subtended by an arc at the centre is ___ the angle subtended by it at any point on the circle.
a) Equal to
b) Double
c) Half
d) Triple
Answer:
b) Double – Theorem 9.7.
Question 8. Angles in the same segment of a circle are always ___.
a) Equal
b) Unequal
c) Supplementary
d) Complementary
Answer:
a) Equal – Theorem 9.8.
Question 9. The angle in a semicircle is always a ___ angle.
a) Acute
b) Obtuse
c) Right
d) Reflex
Answer:
c) Right – Corollary of Theorem 9.8.
Question 10. If a line segment joining two points subtends equal angles at two other points, then all four points are ___.
a) Collinear
b) Concyclic
c) Equal
d) Symmetric
Answer:
b) Concyclic – Theorem 9.9.
Question 11. In a cyclic quadrilateral, the sum of opposite angles is always ___.
a) 90°
b) 120°
c) 150°
d) 180°
Answer:
d) 180° – Theorem 9.10.
Question 12. If the sum of opposite angles of a quadrilateral is 180°, then the quadrilateral is ___.
a) Parallelogram
b) Cyclic
c) Rectangle
d) Square
Answer:
b) Cyclic – Theorem 9.11.
Question 13. The longest chord of a circle is always the ___.
a) Radius
b) Diameter
c) Tangent
d) Secant
Answer:
b) Diameter.
Question 14. Two circles are congruent if they have equal ___.
a) Angles
b) Radii
c) Chords
d) Diameters only
Answer:
b) Radii.
Question 15. Congruent arcs of a circle subtend equal ___ at the centre.
a) Distances
b) Angles
c) Chords
d) Tangents
Answer:
b) Angles.
Question 16. If two arcs of a circle are congruent, then their corresponding chords are ___.
a) Equal
b) Unequal
c) Parallel
d) Perpendicular
Answer:
a) Equal.
Question 17. The perpendicular distance from the centre to the diameter of a circle is always ___.
a) Radius
b) Zero
c) Half radius
d) Equal to chord length
Answer:
b) Zero.
Question 18. A quadrilateral is cyclic if and only if the sum of a pair of its opposite angles is ___.
a) 90°
b) 120°
c) 150°
d) 180°
Answer:
d) 180°.
Question 19. If ∠POQ = 100°, then the angle subtended by arc PQ at a point on the circle is ___.
a) 25°
b) 50°
c) 75°
d) 100°
Answer:
b) 50° – Angle at centre is double angle at circumference.
Question 20. The angle between a chord and a tangent at its end point is equal to the angle subtended by the chord in the ___ segment.
a) Same
b) Alternate
c) Opposite
d) Complementary
Answer:
b) Alternate – Alternate Segment Theorem.
Question 21. The sum of angles in a cyclic quadrilateral ABCD is ___.
a) 180°
b) 270°
c) 360°
d) 540°
Answer:
c) 360°.
Question 22. A diameter subtends a ___ angle at the circumference.
a) 30°
b) 45°
c) 60°
d) 90°
Answer:
d) 90°.
Question 23. If equal chords are drawn in congruent circles, then the chords subtend ___ angles at the centres.
a) Equal
b) Unequal
c) Parallel
d) Reflex
Answer:
a) Equal.
Question 24. The line from the centre of a circle to the midpoint of a chord is always ___ to the chord.
a) Parallel
b) Perpendicular
c) Equal
d) Tangent
Answer:
b) Perpendicular.
Question 25. In a cyclic quadrilateral, if one angle is 70°, the opposite angle is ___.
a) 70°
b) 90°
c) 110°
d) 120°
Answer:
c) 110°.
Question 26. If a chord of a circle is equal to its radius, the angle subtended at the centre is ___.
a) 45°
b) 60°
c) 90°
d) 120°
Answer:
d) 120°.
Question 27. If ∠AOB = 60°, then the angle subtended by chord AB at any point on the circle is ___.
a) 20°
b) 30°
c) 40°
d) 60°
Answer:
b) 30°.
Question 28. If diagonals of a cyclic quadrilateral are diameters of the circle, then the quadrilateral is a ___.
a) Square
b) Rectangle
c) Rhombus
d) Kite
Answer:
b) Rectangle.
Question 29. If two circles intersect at two points, the line joining their centres is the ___ of the common chord.
a) Perpendicular bisector
b) Tangent
c) Secant
d) Parallel line
Answer:
a) Perpendicular bisector.
Question 30. If ∠ACB = ∠ADB, then points A, B, C, D are ___.
a) Collinear
b) Concyclic
c) Parallel
d) Equal
Answer:
b) Concyclic.
Question 31. If in a circle AB = CD, then arcs AB and CD are ___.
a) Congruent
b) Unequal
c) Parallel
d) Perpendicular
Answer:
a) Congruent.
Question 32. The angle subtended by a semicircle at the centre is ___.
a) 90°
b) 120°
c) 150°
d) 180°
Answer:
d) 180°.
Question 33. A cyclic parallelogram is always a ___.
a) Rhombus
b) Rectangle
c) Kite
d) Square
Answer:
b) Rectangle.
Question 34. In a circle, the distance of the longest chord from the centre is always ___.
a) Equal to radius
b) Equal to diameter
c) Zero
d) Infinity
Answer:
c) Zero.
Question 35. If two circles are drawn with diameters as sides of a triangle, then their intersection point lies on the ___ side of the triangle.
a) First
b) Second
c) Third
d) None
Answer:
c) Third.
Fill in the blanks on Circles for Class 9 Maths
1. Equal chords of a circle subtend equal ___ at the centre.
Answer:
angles
2. If two chords of a circle subtend equal angles at the centre, then the chords are ___.
Answer:
equal
3. The perpendicular from the centre of a circle to a chord always ___ the chord.
Answer:
bisects
4. If a line from the centre bisects a chord, then the line is ___ to the chord.
Answer:
perpendicular
5. Equal chords of a circle are equidistant from the ___ of the circle.
Answer:
centre
6. Chords equidistant from the centre of a circle are always ___ in length.
Answer:
equal
7. The angle subtended by an arc at the centre is ___ the angle subtended by it at the circle.
Answer:
double
8. Angles in the same segment of a circle are always ___.
Answer:
equal
9. The angle in a semicircle is always a ___ angle.
Answer:
right
10. If a line segment joining two points subtends equal angles at two other points, then all four points are ___.
Answer:
concyclic
11. In a cyclic quadrilateral, the sum of a pair of opposite angles is always ___.
Answer:
180°
12. If the sum of opposite angles of a quadrilateral is 180°, then the quadrilateral is ___.
Answer:
cyclic
13. The longest chord of a circle is always the ___.
Answer:
diameter
14. Two circles are congruent if they have equal ___.
Answer:
radii
15. Congruent arcs of a circle subtend equal ___ at the centre.
Answer:
angles
16. If two arcs of a circle are congruent, their corresponding chords are ___.
Answer:
equal
17. The angle subtended by a diameter at the circumference is always ___.
Answer:
90°
18. A quadrilateral is cyclic if and only if the sum of a pair of opposite angles is ___.
Answer:
180°
19. The angle subtended by an arc at the centre of a circle is always ___ the angle it subtends on the circumference.
Answer:
twice
20. If a chord is equal to the radius of the circle, then the angle subtended by it at the centre is ___.
Answer:
120°
21. In a cyclic quadrilateral, if one angle is 70°, then the opposite angle is ___.
Answer:
110°
22. The line from the centre of a circle to the midpoint of a chord is always ___ to the chord.
Answer:
perpendicular
23. In a circle, arcs of equal length subtend ___ angles at the centre.
Answer:
equal
24. A cyclic parallelogram is always a ___.
Answer:
rectangle
25. In a circle, the distance of the longest chord from the centre is always ___.
Answer:
zero
