Class 9 Maths Chapter 5, I’m Up and Down, and Round and Round, is the circles chapter of Ganita Manjari. It begins with circles in cave paintings at Gudahandi in Odisha, ripples, sunflowers and the eclipsed sun, and goes on to prove the chord and arc theorems of Class 9 geometry, ending with concyclic points and cyclic quadrilaterals.
What Class 9 Maths Chapter 5 Covers
5.1 Definitions and 5.2 Symmetries of a Circle define centre, radius, chord and arc, and show that a circle has reflection symmetry across every diameter and rotational symmetry through any angle.
5.3 How Many Circles? asks how many circles pass through one, two and three points: infinitely many through two (their centres lie on the perpendicular bisector), and exactly one through three points not on a line, the circumcircle.
5.4 to 5.6 Chords prove that equal chords subtend equal angles at the centre, that the perpendicular from the centre bisects a chord, and that equal chords are equally far from the centre while a longer chord lies closer to it. Paper-folding activities come before each proof.
5.7 Angles Subtended by an Arc and 5.8 Concyclicity of Points show that the angle at the centre is twice the angle at any point on the rest of the circle, and when four points lie on one circle.
Exercises in Chapter 5
- Exercise Sets 5.1 to 5.6 after the sections, plus short in-text exercises such as finding the remaining angles of a cyclic quadrilateral with ∠A = 80°.
- End-of-Chapter Exercises on all the chord, arc and cyclic quadrilateral results.
Read Class 9 Maths Chapter 5 Online
More Chapters
- Previous: Chapter 4: Exploring Algebraic Identities
- Next: Chapter 6: Measuring Space: Perimeter and Area
- Hindi medium: Class 9 Maths Chapter 5 PDF in Hindi
- All Maths chapters and the other Class 9 books: Class 9 NCERT books 2026-27
- All Class 1 to 12 NCERT Textbooks: NCERT Books PDF (Class 1–12)
FAQ
Which chapter of the new Class 9 maths book is on circles?
Chapter 5, I’m Up and Down, and Round and Round, in Ganita Manjari Part I.
How many circles pass through three points?
If the three points are not on one straight line, exactly one: the circumcircle, whose centre is where the perpendicular bisectors of the joining segments meet.