Chapter 10 · Class 10 CBSE · Free Worksheet PDF

Circle Sums for Class 10 — Free CBSE Worksheet PDF with Answers

Download a free printable circles worksheet for Class 10 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 10 — Practice Questions

Here are 8 sample circles sums from this Class 10 CBSE worksheet. Download the full PDF for all 30 questions with answers.

Q1.Which of the following statements correctly defines a tangent to a circle?
A.A line that intersects a circle at two points.
B.A line that passes through the center of a circle.
C.A line that touches a circle at exactly one point.
D.A line segment that connects two points on a circle.

Difficulty: Easy

Q2.From a point P lying inside a circle, how many tangents can be drawn to the circle?
A.Exactly one
B.Exactly two
C.Infinitely many
D.Zero

Difficulty: Easy

Q3.A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q so that OQ = 12 cm. What is the measure of ∠OPQ?
A.30°
B.60°
C.90°
D.180°

Difficulty: Easy

Q4.A student states that if a line AB is tangent to a circle at point P, and OP is a radius, then ∠OPA must be 60°. What is the error in this statement?
A.The angle should be 45°.
B.The angle should be 180°.
C.The angle should be 90°.
D.There is no error, the statement is correct.

Difficulty: Easy

Q5.Which of the following statements about a tangent to a circle is TRUE?
A.A tangent always passes through the center of the circle.
B.The radius drawn to the point of contact is perpendicular to the tangent.
C.A tangent can intersect the circle at two points.
D.The length of a tangent from an external point is always equal to the radius.

Difficulty: Easy

Q6.From an external point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the center is 25 cm. The radius of the circle is:
A.7 cm
B.10 cm
C.12 cm
D.14 cm

Difficulty: Easy

Q7.Two tangents PA and PB are drawn from an external point P to a circle with center O. Which of the following is the correct reason why PA = PB?
A.All tangents from an external point are always equal by definition.
B.Triangles ΔPAO and ΔPBO are congruent.
C.Angles ∠APO and ∠BPO are equal.
D.Radii OA and OB are equal.

Difficulty: Easy

Q8.Consider a circle with center O and a point A on the circle. A line segment OA is drawn. Another line M touches the circle at point A and extends infinitely in both directions. Which statement is correct?
A.OA is a tangent and M is a secant.
B.OA is a radius and M is a tangent.
C.OA is a diameter and M is a chord.
D.OA is a chord and M is a diameter.

Difficulty: Easy

Answer Key — Sample Questions+
Q1:A line that touches a circle at exactly one point.
Q2:Zero
Q3:90°
Q4:The angle should be 90°.
Q5:The radius drawn to the point of contact is perpendicular to the tangent.
Q6:7 cm
Q7:Triangles ΔPAO and ΔPBO are congruent.
Q8:OA is a radius and M is a tangent.

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

About This Worksheet

TopicCircles
BoardCBSE
Class10
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 10?+
You can download a free Circles PDF worksheet for Class 10 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 10 worksheet?+
This SparkEd worksheet for Circles Class 10 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 10 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 10 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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SparkEd Maths provides free printable maths worksheets for Class 1-10 across CBSE, ICSE, IB, Olympiad, UP Board, Maharashtra SSC, and TN Board. Every worksheet includes an answer key and is aligned to the 2025-26 syllabus.