Chapter 5 of the new Ganita Manjari book is Circles. The Class 9 Maths Formula Sheet Chapter 5 Circles brings together the chord rules, the angle relations, and the cyclic quadrilateral facts on one clean page for quick revision.
- Rules inside: about 12 rules, from the chord-length relation to the angle in a semicircle.
- What they cover: chords and distance from the centre, central and inscribed angles, and cyclic quads.
- Why one page helps: the chapter has more rules than formulas, so a single sheet is easy to revise.
This sheet is prepared by subject teachers, matched to the current 2026-27 NCERT, and checked line by line so a Class 9 student can trust every rule.
What Does the Class 9 Maths Circles Formula Sheet Cover?
The Class 9 Maths Formula Sheet Chapter 5 Circles covers the full run of the chapter. You get the radius and diameter relation, the chord-length formula, and the distance of a chord from the centre. It then lists how many circles pass through given points, the equal-chord rules, the perpendicular from the centre, and the angle relations: the central angle is twice the inscribed angle, angles in the same segment are equal, the angle in a semicircle is a right angle, and opposite angles of a cyclic quadrilateral add to 180∘. Since Circles is mostly about relations, the sheet keeps the rules honest to the book.
Video Walkthrough
Source: PW Class 9 - NEEV on YouTube
Circles Class 9 Maths All Formulas at a Glance
The table below lists every rule for Chapter 5. Each math cell is written in clean math so you can use it right away.
| Concept | Formula | What it means |
|---|---|---|
| Radius and diameter | diameter = 2r | The diameter is the longest chord. |
| Length of a chord | = 2√r2 - d2 | d is the distance from the centre. |
| Distance from centre | d = √r2 - (/2)2 | Found from the chord length and radius. |
| Circles through 2 points | infinitely many | Centres lie on the perpendicular bisector. |
| Circle through 3 points | unique if non-collinear | This is the circumcircle. |
| Equal chords | equal central angles | Equal chords are the same distance from the centre. |
| Perpendicular from centre | bisects the chord | The centre-to-midpoint line is at 90∘. |
| Longer vs shorter chord | longer chord is nearer the centre | Distance from the centre falls as the chord grows. |
| Angle: centre vs circle | = 2 | On the same arc. |
| Same segment | angles are equal | Angles on the same arc match. |
| Angle in a semicircle | 90∘ | The diameter subtends a right angle. |
| Cyclic quadrilateral | opposite angles sum to 180∘ | The exterior angle equals the interior opposite. |
When to Use Which Rule in Circles
Pick the right rule by reading what the figure shows. This short list keeps the choice quick.
- If you know the radius and the distance to a chord, use = 2√r2 - d2.
- If a line from the centre meets a chord, remember it bisects the chord.
- If two chords are equal, they are equally far from the centre.
- If an angle sits at the centre and another on the circle, the centre angle is twice as big.
- If a triangle uses the diameter, the angle facing it is 90∘.
- If four points lie on a circle, opposite angles add to 180∘.
Quick Facts for Circles
The cards below hold the facts students forget most. Keep the Class 9 Maths Formula Sheet Chapter 5 Circles next to them while you revise, and the rules will settle faster.
How will Collegedunia's Formula Sheet Help You with Circles?
Collegedunia builds the Class 9 Maths Formula Sheet Chapter 5 Circles as one printable page for fast revision.
- 2026-27 Ganita Manjari match: Every rule follows the new book, not the old chapter order.
- Plain meaning added: Each rule has a short line saying what it does.
- Teacher checked: Subject experts verify each chord, angle, and cyclic-quad rule.
- Free PDF: Download the sheet and keep it ready for your Class 9 annual exam.
More Circles Maths Class 9 Resources
Use the links below to open the other Collegedunia resources for this chapter.
NCERT Formula Sheet for Class 9 Maths: All Chapters
Use the table below to open the Formula Sheet for any other chapter of the new Class 9 Maths book.
| Chapter | Resource |
|---|---|
| Chapter 1 | Coordinates Formula Sheet |
| Chapter 2 | Linear Polynomials Formula Sheet |
| Chapter 3 | The World of Numbers Formula Sheet |
| Chapter 4 | Algebraic Identities Formula Sheet |
| Chapter 5 | Circles Formula Sheet |
| Chapter 6 | Perimeter and Area Formula Sheet |
| Chapter 7 | Introduction to Probability Formula Sheet |
| Chapter 8 | Sequences and Progressions Formula Sheet |
Circles Class 9 Maths Formula Sheet FAQs
Ques. Where can I download the Circles Class 9 Maths Formula Sheet PDF?
Ans. You can download the Circles Class 9 Maths Formula Sheet PDF directly from this page. Both the Normal and HD versions are free.
Ques. How many rules are in the Class 9 Maths Chapter 5 Circles Formula Sheet?
Ans. The sheet lists about 12 rules, covering chords, distance from the centre, central and inscribed angles, and cyclic quadrilaterals.
Ques. Is this chapter part of the new 2026-27 Ganita Manjari book?
Ans. Yes. Circles is Chapter 5 of the new Ganita Manjari book for the 2026-27 syllabus. It keeps the chord and angle theorems from the older Circles chapter.
Ques. How many pages is the Circles Formula Sheet PDF?
Ans. The Formula Sheet PDF runs about 2 pages, with a full rule table and a quick-reference section for last-day revision.
Ques. What is the main angle rule on this sheet?
Ans. The main rule is that the angle at the centre is twice the angle at the circle on the same arc, and the semicircle case gives a right angle.
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