Chapter 10 · Class 9 CBSE · Free Worksheet PDF

Circle Sums for Class 9 — Free CBSE Worksheet PDF with Answers

Download a free printable circles worksheet for Class 9 CBSE with 30 practice questions covering circle properties, area and circumference, tangent, chord, arc, sector, and segment problems. Includes complete answer key. CBSE-aligned for the 2025-26 syllabus.

Last updated: 5 May 2026

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30 questions (Easy + Medium + Hard) with answer key. Fresh set generated daily.

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Sample Circles Sums for Class 9 — Practice Questions

Here are 8 sample circles sums from this Class 9 CBSE worksheet. Download the full PDF for all 30 questions with answers.

Q1.Which of the following statements correctly defines a 'segment' of a circle?
A.A) The region between an arc and two radii joining the center to the endpoints of the arc.
B.B) The region between a chord and its corresponding arc.
C.C) The entire boundary of the circle.
D.D) A line segment connecting two points on the circle.

Difficulty: Easy

Q2.In a circle, if two chords AB and CD are equal in length, which of the following statements must be true?
A.A) They are parallel to each other.
B.B) They subtend equal angles at the center of the circle.
C.C) They are equidistant from the center.
D.D) Both B and C.

Difficulty: Easy

Q3.A chord of length 16 cm is drawn in a circle with a radius of 10 cm. What is the distance of the chord from the center of the circle?
A.A) 6 cm
B.B) 8 cm
C.C) 10 cm
D.D) 12 cm

Difficulty: Easy

Q4.Ravi was asked to prove that if a line segment from the center of a circle bisects a chord, then it is perpendicular to the chord. He started by assuming the line is perpendicular and then proved it bisects the chord. Where did Ravi make a mistake in his reasoning?
A.A) He used the Pythagorean theorem incorrectly.
B.B) He assumed what he needed to prove (circular reasoning).
C.C) He did not draw a diagram.
D.D) He should have used similar triangles.

Difficulty: Easy

Q5.Consider two chords in a circle. Chord P is 8 cm long and is 3 cm away from the center. Chord Q is 6 cm long. Which of the following statements about Chord Q's distance from the center is true?
A.A) It is less than 3 cm.
B.B) It is equal to 3 cm.
C.C) It is greater than 3 cm.
D.D) It cannot be determined without the radius.

Difficulty: Easy

Q6.Which of the following statements is TRUE?
A.A) An infinite number of circles can pass through three collinear points.
B.B) Exactly one circle can pass through three non-collinear points.
C.C) No circle can pass through two distinct points.
D.D) A unique circle can be drawn through any four points.

Difficulty: Easy

Q7.In a circle with center O, points A, B, and C are on the circumference. If ∠AOB = 80°, what is the measure of ∠ACB?
A.A) 40°
B.B) 80°
C.C) 160°
D.D) 20°

Difficulty: Easy

Q8.Points A, B, C, D are on a circle. If ∠CAD = 35° and ∠ACB = 40°, what is the measure of ∠CBD?
A.A) 35°
B.B) 40°
C.C) 75°
D.D) 5°

Difficulty: Easy

Answer Key — Sample Questions+
Q1:B) The region between a chord and its corresponding arc.
Q2:D) Both B and C.
Q3:A) 6 cm
Q4:B) He assumed what he needed to prove (circular reasoning).
Q5:C) It is greater than 3 cm.
Q6:B) Exactly one circle can pass through three non-collinear points.
Q7:A) 40°
Q8:A) 35°

Download the full PDF for all 30 answers with step-by-step solutions.

About This Worksheet

TopicCircles
BoardCBSE
Class9
Total Questions30 (10 Easy + 10 Medium + 10 Hard)
Answer KeyIncluded
PriceFree

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Frequently Asked Questions

Where can I download free circles sums for Class 9?+
You can download a free Circles PDF worksheet for Class 9 CBSE right here on SparkEd. The worksheet includes 30 practice questions (circle properties, area and circumference, tangent, chord, arc, sector, and segment problems) at easy, medium, and hard levels with a complete answer key.
How many circles questions are in this Class 9 worksheet?+
This SparkEd worksheet for Circles Class 9 contains 30 questions — 10 easy, 10 medium, and 10 hard. The questions cover circle properties, area and circumference, tangent, chord, arc, sector, and segment problems. A fresh set is generated daily so students never repeat the same sheet.
Does the Circles worksheet for Class 9 include answers?+
Yes! Every SparkEd worksheet comes with a complete answer key. Students can self-check their work after completing the sheet. The PDF is free to download and print.
Is this circles worksheet aligned to CBSE syllabus?+
Yes. This worksheet is specifically designed for Class 9 CBSE students and aligned to the 2025-26 CBSE syllabus. All questions follow the CBSE exam pattern and difficulty level.
Can I print this Circles worksheet?+
Absolutely! The worksheet downloads as an A4-size PDF that is ready to print. It includes the questions, space for working, and a separate answer key — perfect for classroom use or home practice.
How is this worksheet different from NCERT textbook exercises?+
SparkEd worksheets go beyond NCERT exercises by providing 30 questions at 3 progressive difficulty levels. Level 1 (Easy) builds confidence, Level 2 (Medium) tests application, and Level 3 (Hard) prepares for exams. Each worksheet includes word problems and conceptual questions, not just computation.

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