The NCERT Solutions Class 9 Maths Chapter 5 Circles cover every question from the new Ganita Manjari book. This chapter builds on the compass and ruler work you already know. It teaches you how to draw circumcircles, study chords, and use the chord length rule with clear steps.

Chapter 5 Circles — Exercise-wise NCERT Solutions

  • Exercises solved: Exercise Sets 5.1 to 5.6 and all 26 End-of-Chapter problems
  • Main skills: drawing circumcircles, chord properties, and the chord length formula
  • Why it matters: it prepares you for circle theorems in the Class 10 syllabus

These solutions are prepared by subject teachers, matched to the current 2026-27 NCERT, and checked step by step so a Class 9 student can follow each line.

Table of Contents

  1. What Does Chapter 5 Circles Cover
  2. Chapter 5 Circles Exercise-Wise Breakdown
  3. Common Mistakes Students Make in Circles
  4. Sample Solved Question from Chapter 5
  5. How to Study Circles & Time Needed
  6. How Collegedunia's NCERT Solutions Help You with Circles
  7. More Circles Maths Resources
  8. NCERT Solutions: All Chapters

What Does Class 9 Maths Chapter 5 Circles Cover?

The chapter starts with a simple idea. Every point on a circle sits at the same distance from the centre. Chapter 5 uses this to draw the circumcircle of a triangle and to study chords. You learn why a perpendicular from the centre bisects a chord, and why equal chords stay the same distance from the centre. The NCERT Solutions Class 9 Maths Chapter 5 Circles then show how to find any chord length using 2√r2 - d2.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Class 9 Maths Chapter 5 Circles Exercise-Wise Breakdown

The chapter has six exercise sets and one long End-of-Chapter set. The table below shows what each part asks, so you can plan your practice.

ExerciseQuestionsWhat it covers
Exercise Set 5.14Drawing circumcircles and finding the circumcentre
Exercise Set 5.22Isosceles triangle formed by a chord and the centre
Exercise Set 5.33Perpendicular from the centre bisecting a chord
Exercise Set 5.43Equal chords staying equidistant from the centre
Exercise Set 5.53Using the chord length formula
Exercise Set 5.63Central angles and cyclic quadrilaterals
End-of-Chapter Exercises26Mixed problems on all circle properties

Common Mistakes Students Make in Circles

Most errors in this chapter come from small slips, not hard ideas. Fix these early and your marks stay safe.

Watch Out: Students often use the full chord length as one side of the right triangle. You must use half the chord, because the perpendicular from the centre bisects it, or the answer comes out wrong.
  • Forgetting that the radius, not the diameter, is the distance from the centre.
  • Placing the circumcentre inside every triangle, even an obtuse one.
  • Skipping the square root at the end of a chord length sum.

Sample Solved Question from Class 9 Maths Chapter 5

Here is one Exercise Set 5.5 question, solved step by step, so you can see the method.

Question: Find the length of a chord of a circle where the radius is 7 cm and the perpendicular distance from the centre is 6 cm.

Step 1. Write the chord length rule. A chord at distance d from the centre has length 2√r2 - d2.

Step 2. Put in the values. Here r = 7 and d = 6, so the length is 2√72 - 62.

Step 3. Simplify inside the root: 2√49 - 36 = 2√13.

Final answer. The chord is 2√13 cm, which is about 7.2 cm.

Quick Tip: Always draw the radius to the chord end and the perpendicular to its midpoint. This makes the right triangle easy to spot.

How to Study Circles and Time Needed

This chapter mixes drawing with short proofs. If you draw as you read, it goes fast. Start with the six exercise sets, then use the NCERT Solutions Class 9 Maths Chapter 5 Circles to check your End-of-Chapter answers.

Revision mode

2-3 hours

If you have done this chapter once and are revising.

First-read

5-7 hours

If you are reading Circles for the first time.

How will Collegedunia's NCERT Solutions Help You with Circles?

Collegedunia gives you the full NCERT Solutions Class 9 Maths Chapter 5 Circles as clean, step-by-step answers in one place.

  • 2026-27 Ganita Manjari match: Every answer follows the new book, not the old chapter list.
  • Full working shown: Each step is written out, so you never guess how a line was reached.
  • Teacher checked: Subject experts verify each drawing, chord, and proof.
  • Free PDF: Download the solutions and revise offline before your exam.

More Circles Maths Class 9 Resources

NCERT Solutions for Class 9 Maths: All Chapters

Use the table below to open the NCERT Solutions for any other chapter of the new Class 9 Maths book.

ChapterResource
Chapter 1Coordinates NCERT Solutions
Chapter 2Linear Polynomials NCERT Solutions
Chapter 3The World of Numbers NCERT Solutions
Chapter 4Algebraic Identities NCERT Solutions
Chapter 5Circles NCERT Solutions
Chapter 6Perimeter and Area NCERT Solutions
Chapter 7Introduction to Probability NCERT Solutions
Chapter 8Sequences and Progressions NCERT Solutions

Circles Class 9 Maths NCERT Solutions FAQs

Ques. Where can I download Circles Class 9 Maths NCERT Solutions PDF?

Ans. You can download the Circles Class 9 Maths NCERT Solutions PDF directly from this page. Both the Normal and HD versions are free.

Ques. Is this chapter part of the new Class 9 Maths book?

Ans. Yes. Circles is Chapter 5 of the new Ganita Manjari book for the 2026-27 syllabus. It sits between Algebraic Identities and Perimeter and Area.

Ques. How many exercises are there in Class 9 Maths Chapter 5?

Ans. There are six exercise sets, 5.1 to 5.6, and a set of 26 End-of-Chapter problems. Collegedunia solves all of them.

Ques. What is the chord length formula in this chapter?

Ans. A chord at a perpendicular distance d from the centre of a circle with radius r has length 2√r2 - d2. Chapter 5 uses this rule often.

Ques. Is the Class 9th Maths Circles solutions PDF hard to follow?

Ans. No. Each answer is written in short steps with a diagram where needed, so a Class 9 student can read it on the first try.