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JAC • Class 6 • Mathematics • Ch 13

Estimated Time: 45 Mins

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Circle

Identify a circle’s centre, radius, diameter, chord, arc, sector and segment.

View All Chapters JCERT Hindi Textbook

Overview Core Concepts Solved Examples Common Traps Summary Self Check Take MCQ Test

Why This Chapter Matters

Identify a circle’s centre, radius, diameter, chord, arc, sector and segment.

Before You Begin (Prerequisites)

Familiarity with simple shapes and measurement

What You Will Learn (Core Objectives)

Identify a circle’s centre, radius, diameter, chord, arc, sector and segment.

Chapter Roadmap & Progression

1 Syllabus and book alignment

2 Concept 1

3 Concept 2

4 Concept 3

Complete Concept Guide (100% Curriculum Coverage)

Syllabus and book alignment

JCERT 2026–27: Regular schools (Non-SOE) — Chapter 13 · Circle. Syllabus pages 217–222. These notes follow this topic. Official syllabus. Official JCERT Hindi textbook. Some source PDFs are damaged. The supplementary reference uses different chapter numbering.

Concept 1

A circle is the set of all points in a plane at a fixed distance from a fixed point called the centre. The fixed distance is the radius. A diameter passes through the centre and joins two points of the circle.

Concept 2

A chord joins any two points of the circle. A diameter is its longest chord. An arc is part of the circular boundary; a semicircle is half of that boundary. All radii of the same circle are equal.

Concept 3

A sector is bounded by two radii and an arc, like a pizza slice. A segment is bounded by a chord and its corresponding arc. The centre lies inside the circle; it is not on its boundary.

Conceptual Solved Examples & Case Studies

Example 1

If a circle’s radius is 4 cm, find its diameter.

Step-by-Step Solution:

Diameter = 2 × radius = 2 × 4 = 8 cm.

Common Misconceptions & Examiner Traps

Common Misconception

Common misconception

Scientific Reality & Correction

Every diameter is a chord, but a chord need not pass through the centre.

Chapter Summary & 10 Key Takeaways

Takeaway 1

Takeaway 2

A chord joins any two points of the circle. A diameter is its longest chord. An arc is part of the circular boundary; a semicircle is half of that boundary. All radii of the same circle are equal.

Takeaway 3

A sector is bounded by two radii and an arc, like a pizza slice. A segment is bounded by a chord and its corresponding arc. The centre lies inside the circle; it is not on its boundary.

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

A circle has diameter 14 cm. What is its radius?

Reveal Answer & Explanation

Answer: Radius = diameter ÷ 2 = 14 ÷ 2 = 7 cm.
Use the definition above.

Chapter practice

CBT tests for this chapter are not published yet. Solve the self-check questions above and compare your answers.

All Class 6 Mathematics Chapters

Ch 1: Knowing Our Numbers Ch 2: Whole Numbers Ch 3: Integers Ch 4: Playing with Numbers Ch 5: Fractions Ch 6: Decimals Ch 7: Ratio and Proportion Ch 8: Algebra Ch 9: Line, Line Segment and Ray Ch 10: Pairs of Lines Ch 11: Angles Ch 12: Polygons Ch 13: Circle Ch 14: Three-Dimensional Shapes Ch 15: Symmetry Ch 16: Practical Geometry Ch 17: Perimeter and Area Ch 18: Data Handling

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