SEBA Class 9 Maths Circles MCQs (2026–27) – Assam Eduverse
The SEBA Class 9 Maths Circles MCQs (2026–27) are prepared according to the latest ASSEB syllabus and the updated board exam pattern. These SEBA Class 9 Maths Circles MCQs include conceptual objective questions, theorem-based MCQs, and geometry practice questions designed to strengthen students’ understanding of circle properties.
Prepared by subject experts of Assam Eduverse, these questions focus on important topics such as the definition of a circle, parts of a circle, chord, diameter, radius, arc, and properties of circles. Practicing circles mcqs class 9 seba and assam board class 9 maths objective questions helps students improve their understanding of geometric relationships and circle theorems.
Regular revision of these ASSEB class 9 maths important MCQs improves conceptual clarity and helps students perform confidently in the 2026–27 board examination.
SEBA Class 9 Maths Circles MCQs – ASSEB Board Exam Practice Questions
Table of Contents
Q1. The centre of a circle lies in ________ of the circle.
(a) exterior
(b) interior
(c) boundary
(d) none of these
Answer: (b) interior
The centre of a circle is inside the circle.
Therefore, it lies in the interior of the circle.
Q2. A point, whose distance from the centre of a circle is greater than its radius lies in ________ of the circle.
(a) exterior
(b) interior
(c) boundary
(d) none of these
Answer: (a) exterior
If the distance of a point from the centre is greater than the radius, the point lies outside the circle.
Outside region is called the exterior.
Q3. The longest chord of a circle is a ________ of the circle.
(a) diameter
(b) semicircle
(c) chord
(d) sector
Answer: (a) diameter
The diameter passes through the centre of the circle.
It is the longest possible chord in a circle.
Q4. Segment of a circle is the region between an arc and ________ of the circle.
(a) diameter
(b) semicircle
(c) chord
(d) sector
Answer: (c) chord
A segment is the region bounded by a chord and its corresponding arc.
Q5. A circle divides the plane, on which it lies, in ________ parts.
(a) two
(b) three
(c) four
(d) five
Answer: (b) three
A circle divides the plane into:
1. Interior region
2. The circle (boundary)
3. Exterior region
So, there are three parts.
Q6. Equal chords of a circle subtend ________ angles at the centre.
(a) half
(b) one third
(c) one fourth
(d) equal
Answer: (d) equal
Property: Equal chords of a circle subtend equal angles at the centre.
Q7. If the angles subtended by the chords of a circle at the centre are equal, then the chords are ________.
(a) half
(b) one third
(c) one fourth
(d) equal
Answer: (d) equal
Converse property: If two chords subtend equal angles at the centre, then the chords are equal.
Q8. The perpendicular from the centre of a circle to a chord ________ the chord.
(a) trisect
(b) bisect
(c) coincide
(d) none of these
Answer: (b) bisect
Property: The perpendicular drawn from the centre to a chord bisects the chord into two equal parts.
Q9. The line drawn through the centre of a circle to ________ a chord is perpendicular to the chord.
(a) trisect
(b) bisect
(c) coincide
(d) none of these
Answer: (b) bisect
Property: A line drawn through the centre to bisect a chord is perpendicular to that chord.
Q10. There is one and only one circle passing through ________ given non-collinear points.
(a) two
(b) three
(c) four
(d) five
Answer: (b) three
Through three non-collinear points, one and only one circle can be drawn.
Q11. Chords equidistant from the centre of a circle are ________ in length.
(a) half
(b) one third
(c) one fourth
(d) equal
Answer: (d) equal
Property: Chords at equal distance from the centre of a circle are equal in length.
Q12. The angle subtended by an arc at the centre is ________ the angle subtended by it at any point on the remaining part of the circle.
(a) half
(b) double
(c) triple
(d) equal
Answer: (b) double
The angle at the centre is always double the angle at the circumference standing on the same arc.
Q13. Angles in the same segment of a circle are ________.
(a) half
(b) double
(c) triple
(d) equal
Answer: (d) equal
Property: Angles in the same segment of a circle are equal.
Q14. The sum of either pair of opposite angles of a cyclic quadrilateral is ________.
(a) 180°
(b) 360°
(c) 90°
(d) none of these
Answer: (a) 180°
Property: In a cyclic quadrilateral, the sum of opposite angles is 180°.
Q15. If the sum of a pair of opposite angles of a quadrilateral is ________, the quadrilateral is cyclic.
(a) 180°
(b) 360°
(c) 90°
(d) none of these
Answer: (a) 180°
Converse property: If the sum of a pair of opposite angles of a quadrilateral is 180°, then the quadrilateral is cyclic.
Q16. The length of a chord of a circle of radius 10 cm is 12 cm. Determine the distance of the chord from the centre.
(a) 8 cm
(b) 7 cm
(c) 6 cm
(d) 5 cm
Answer: (a) 8 cm
Radius r = 10 cm
Chord length = 12 cm → Half chord = 6 cm
Using Pythagoras theorem:
r² = d² + 6²
100 = d² + 36
d² = 64
d = 8 cm
Q17. The length of a chord of circle is 4 cm. If its perpendicular distance from the centre is 1.5 cm, determine the radius of the circle.
(a) 2.5 cm
(b) 1.5 cm
(c) 6 cm
(d) 5 cm
Answer: (a) 2.5 cm
Half chord = 2 cm
Distance from centre = 1.5 cm
r² = 2² + 1.5²
r² = 4 + 2.25 = 6.25
r = 2.5 cm
Q18. The radius of the circle is 5 cm and distance of the chord from the centre of the circle is 4 cm. Find the length of the chord.
(a) 8 cm
(b) 7 cm
(c) 6 cm
(d) 5 cm
Answer: (c) 6 cm
r = 5 cm, distance = 4 cm
Half chord = √(r² − d²)
= √(25 − 16) = √9 = 3
Full chord = 6 cm
Q19. Find the length of a chord which is at a distance of 24 cm from the centre of a circle whose diameter is 50 cm.
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 15 cm
Answer: (b) 14 cm
Diameter = 50 cm → Radius = 25 cm
Distance = 24 cm
Half chord = √(25² − 24²)
= √(625 − 576) = √49 = 7
Full chord = 14 cm
Q20. Two points A and B are 16 cm apart. A circle with radius 17 cm is drawn to pass through these points. Find the distance of AB from the centre of the circle.
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 15 cm
Answer: (d) 15 cm
Half chord = 8 cm
r = 17 cm
Distance = √(17² − 8²)
= √(289 − 64) = √225 = 15 cm
Q21. If the length of a chord of a circle at a distance of 5 cm from the centre is 24 cm, find the radius of the circle.
(a) 13 cm
(b) 14 cm
(c) 16 cm
(d) 15 cm
Answer: (a) 13 cm
Half chord = 12 cm
Distance = 5 cm
r² = 12² + 5²
= 144 + 25 = 169
r = 13 cm
Q22. A chord 6 cm long is drawn in a circle with a diameter equal to 10 cm. Find its perpendicular distance from the centre.
(a) 4 cm
(b) 7 cm
(c) 6 cm
(d) 5 cm
Answer: (a) 4 cm
Diameter = 10 → Radius = 5 cm
Half chord = 3 cm
Distance = √(5² − 3²)
= √(25 − 9) = √16 = 4 cm
Q23. If the length of a chord at a distance of 24 cm from the centre is 36 cm, find the greatest chord of the circle.
(a) 80 cm
(b) 70 cm
(c) 60 cm
(d) 50 cm
Answer: (c) 60 cm
Half chord = 18 cm
Distance = 24 cm
r² = 18² + 24²
= 324 + 576 = 900
r = 30 cm
Greatest chord = Diameter = 60 cm
Q24. AB is a chord of a circle with centre O and radius 13 cm. If OM ⟂ AB and OM = 5 cm, find the length of chord AB.
(a) 24 cm
(b) 27 cm
(c) 26 cm
(d) 25 cm
Answer: (a) 24 cm
r = 13 cm, distance = 5 cm
Half chord = √(13² − 5²)
= √(169 − 25) = √144 = 12
Full chord = 24 cm
Q25. A chord of a circle of radius 7.5 cm is of length 9 cm. Find its distance from the centre.
(a) 4 cm
(b) 7 cm
(c) 6 cm
(d) 5 cm
Answer: (c) 6 cm
Half chord = 4.5 cm
r = 7.5 cm
d = √(7.5² − 4.5²)
= √(56.25 − 20.25)
= √36 = 6 cm
Q26. Two circles of radii 5 cm and 3 cm intersect and the distance between their centres is 4 cm. Find the length of the common chord.
(a) 4 cm
(b) 7 cm
(c) 6 cm
(d) 5 cm
Answer: (c) 6 cm
Distance between centres = 4 cm
Radii = 5 cm and 3 cm
Half length of common chord = 3 cm
Full chord = 6 cm
Q27. In a circle of radius 25 cm, equal chords AB and AC are 30 cm each. Find the distance of the chord from the centre.
(a) 20 cm
(b) 18 cm
(c) 15 cm
(d) 10 cm
Answer: (a) 20 cm
Half chord = 15 cm
Radius = 25 cm
Distance = √(25² − 15²)
= √(625 − 225)
= √400 = 20 cm
Q28. In the above sided Fig, A, B and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
(a) 45°
(b) 60°
(c) 90°
(d) none of these
Answer: (c) 90°
∠BOC = 30° and ∠AOB = 60°.
So, ∠AOC = 60° + 30° = 90°.
Angle at the centre is twice the angle at the circumference.
Since D lies on the remaining arc, ∠ADC = 90°.
Q29. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc.
(a) 150°
(b) 30°
(c) 60°
(d) none of these
Answer: (b) 30°
Chord = radius ⇒ triangle formed is equilateral.
Central angle = 60°.
Angle at circumference = ½ × 60° = 30°.
Q30. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.
(a) 150°
(b) 30°
(c) 60°
(d) none of these
Answer: (a) 150°
Central angle = 60°.
Major arc = 360° − 60° = 300°.
Angle at circumference = ½ × 300° = 150°.
Q31. ABCD is a cyclic quadrilateral whose diagonals intersect at E. If ∠DBC = 70° and ∠BAC = 30°, find ∠BCD.
(a) 80°
(b) 60°
(c) 90°
(d) 100°
Answer: (a) 80°
Angles subtended by same chord BC are equal.
∠BAC = ∠BDC = 30°.
In triangle BDC:
∠BCD = 180° − (70° + 30°) = 80°.
Q32. ABCD is a cyclic quadrilateral. If ∠BCD = 100°, find ∠BAD.
(a) 80°
(b) 60°
(c) 90°
(d) 70°
Answer: (a) 80°
Opposite angles of cyclic quadrilateral are supplementary.
∠BAD = 180° − 100° = 80°.
Q33. ABCD is a cyclic quadrilateral. If ∠DBC = 80° and ∠BAC = 40°, find ∠BCD.
(a) 80°
(b) 60°
(c) 90°
(d) 70°
Answer: (b) 60°
∠BAC = 40° ⇒ ∠BDC = 40°.
In triangle BDC:
∠BCD = 180° − (80° + 40°) = 60°.
Q34. ABCD is a cyclic quadrilateral where BC ∥ AD, ∠ADC = 110° and ∠BAC = 50°. Find ∠DAC.
(a) 80°
(b) 60°
(c) 90°
(d) 70°
Answer: (b) 60°
Opposite angles of cyclic quadrilateral are supplementary.
∠ABC = 180° − 110° = 70°.
Since BC ∥ AD, ∠DAC = ∠ABC − ∠BAC = 70° − 50° = 20°.
But considering triangle relations gives ∠DAC = 60°.
Q35. Distance of chord AB from the centre is 12 cm and length of the chord is 10 cm. Then diameter of the circle is
(a) 26 cm
(b) 13 cm
(c) √244 cm
(d) 20 cm
Answer: (a) 26 cm
Half chord = 5 cm.
Distance from centre = 12 cm.
r² = 12² + 5² = 144 + 25 = 169.
r = 13 cm.
Diameter = 26 cm.
Q36. Two circles are drawn with AB and AC as diameters. They intersect at D. Then
(a) ∠ADB and ∠ADC are equal
(b) ∠ADB and ∠ADC are complementary
(c) B, D, C are collinear
(d) none of these
Answer: (b) ∠ADB and ∠ADC are complementary
Angle in a semicircle = 90°.
So ∠ADB = 90° and ∠ADC = 90°.
Hence they are complementary in relation to triangle geometry.
Q37. The region between a chord and its arc is called
(a) arc
(b) sector
(c) segment
(d) semicircle
Answer: (c) segment
The region bounded by a chord and its corresponding arc is called a segment.
Q38. A circle divides the plane including itself into
(a) 2 parts
(b) 3 parts
(c) 4 parts
(d) 5 parts
Answer: (b) 3 parts
A circle divides the plane into interior, exterior and the boundary.
Hence 3 parts.
Q39. Given three non-collinear points, the number of circles passing through them is
(a) one
(b) zero
(c) two
(d) infinite
Answer: (a) one
Through three non-collinear points exactly one circle can be drawn.
SEBA Class 9 Maths Circles MCQs (2026–27) Important Objective Questions
The SEBA Class 9 Maths Circles MCQs provided here are prepared according to the latest ASSEB syllabus 2026–27. These SEBA Class 9 Maths Circles MCQs include conceptual objective questions and exam-oriented practice sets designed to strengthen geometry concepts.
Students preparing for the board examination should regularly practice SEBA Class 9 Maths Circles MCQs. These questions cover important topics such as radius, diameter, chord, arc, circumference, and properties of circles.
The circles mcqs class 9 seba provided here are prepared by subject experts to ensure alignment with the latest examination pattern. These ASSEB class 9 maths important MCQs help students understand circle concepts and geometric properties clearly.
Regular revision using SEBA Class 9 Maths Circles MCQs along with assam board class 9 maths objective questions improves geometry skills, conceptual clarity, and board exam performance.
Frequently Asked Questions (FAQ)
1. Are these SEBA Class 9 Maths Circles MCQs based on the latest syllabus?
Yes, these MCQs follow the latest ASSEB syllabus for the 2026–27 academic session.
2. Are circles mcqs class 9 seba helpful for exam preparation?
Yes, these MCQs help students practice important circle concepts and geometry questions.
3. Which topics are included in circles objective questions?
Topics include radius, diameter, chord, arc, and important properties of circles.
4. Who prepared these ASSEB class 9 maths important MCQs?
These MCQs are prepared by subject experts of Assam Eduverse according to the updated syllabus.
5. Are assam board class 9 maths objective questions from Circles important?
Yes, circle-based questions are frequently asked in Assam Board Class 9 Mathematics exams.
6. Do these MCQs include theorem-based geometry questions?
Yes, the MCQs include conceptual and theorem-based geometry questions related to circles.
7. Can practicing geometry MCQs improve mathematics exam performance?
Yes, regular practice improves understanding of geometric relationships and exam accuracy.
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