SEBA Class 9 Maths Circles MCQs (2026–27) – Assam Eduverse
The SEBA Class 9 Maths Circles MCQs are structured according to the latest ASSEB syllabus and follow the current academic session’s exam pattern. These SEBA Class 9 Maths Circles MCQs include conceptual, theorem-based, and geometry-focused questions designed to build a strong understanding of circle properties. Students can also explore important maths MCQs chapter-wise for wider practice.
Prepared by subject experts of Assam Eduverse, this collection covers key topics such as the definition and parts of a circle, chord, diameter, radius, arc, and important circle properties. Practicing circles mcqs class 9 seba along with chapterwise MCQs and question answers helps improve understanding of geometric relationships and theorems.
Consistent practice of these ASSEB class 9 maths important MCQs enhances conceptual clarity and builds confidence for the board examination. Students can also refer to complete Class 9 study materials for comprehensive preparation.
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 – Important Objective Questions
A strong understanding of Circles is essential for mastering geometry in Class 9 Mathematics. Regular practice of MCQs based on the latest SEBA (ASSEB) syllabus helps students build clarity in concepts and become familiar with the types of objective questions commonly asked in examinations.
These SEBA Class 9 Maths Circles MCQs focus on key concepts such as radius, diameter, chord, arc, circumference, and important properties of circles. Since geometry requires both conceptual understanding and visualization, solving such questions regularly helps students develop accuracy and confidence.
Practicing these important objective questions for Class 9 Maths also improves problem-solving skills and helps students quickly identify correct answers in exam situations. It reduces confusion between similar terms and strengthens the overall understanding of geometric relationships.
Another key benefit of consistent MCQ practice is improved speed and precision. Students learn to approach questions logically, avoid common mistakes, and manage their time effectively during exams. This makes revision more efficient and less stressful.
To perform well in school exams and board-based assessments, students should make these MCQs a regular part of their study routine. With clear concepts and continuous practice, scoring well in the Circles chapter becomes much easier and more achievable.
FAQs – SEBA Class 9 Maths Circles MCQs
1. How many MCQs come from Circles in SEBA Class 9 Maths exam?
Usually 3–5 MCQs come from Circles within the 45 MCQs pattern. Focus on definitions and properties—they are frequently asked.
2. Which topics are most important in SEBA Class 9 Maths Circles MCQs?
Key topics include radius, diameter, chord, arc, and central angles. Learn definitions clearly—most MCQs are concept-based, not lengthy calculations.
3. Where can I download SEBA Class 9 Maths Circles MCQs with answers PDF?
You can download chapter-wise MCQs from Assam Eduverse. Practice daily and revise mistakes—it really improves exam confidence.
4. Are SEBA Class 9 Maths Circles MCQs difficult for exams?
No, they are usually easy if concepts are clear. Most questions test basic understanding, so revise NCERT examples properly.
5. How to prepare fast for Circles MCQs before exam?
Revise formulas and solve 20–30 MCQs daily. Focus on previous papers—many questions repeat in similar patterns.
6. Do previous year questions help in SEBA Class 9 Circles MCQs?
Yes, very helpful. Many MCQs follow similar patterns. Assam Eduverse provides useful practice sets based on past trends.
7. What are common mistakes students make in Circles MCQs?
Students confuse radius, diameter, and chord. Always read questions carefully and avoid rushing during the MCQ section.
🎓 About Assam Eduverse
Assam Eduverse is a dedicated learning platform committed to providing high-quality academic resources for students affiliated with SEBA, AHSEC (ASSEB), SCERT, and CBSE.
We provide chapter-wise notes, detailed solutions, MCQs, important questions, and previous year papers for Classes 9 to 12. All content is carefully curated in alignment with the latest Assam Board syllabus and reflects current examination patterns.
Our resources are designed to simplify complex concepts, encourage consistent practice, and help students achieve better results in their board examinations. Materials are available in both Assamese and English mediums to cater to diverse learning preferences.
Discover MCQs, study materials, solutions, and exam preparation guides to enhance your preparation and strengthen your revision strategy.