Download I’m Up and Down, and Round and Round – NCERT Class 9 Maths Chapter 5 PDF from the new NCERT Class 9 Maths book Ganita Manjari (2026-27). Read the chapter online or download the free PDF. A circle is the locus of points at a fixed distance (the radius) from a fixed point (the centre). Every diameter is a line of reflection symmetry, and the circle has rotational symmetry about its centre through any angle.
I’m Up and Down, and Round and Round PDF – Chapter 5 of Ganita Manjari (Part I)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 5 PDF | I'm Up and Down, and Round and Round | View PDF |
| Full book | NCERT Class 9 Maths – Ganita Manjari | View Book |
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What Is in I’m Up and Down, and Round and Round? (Class 9 Maths Chapter 5)
- A circle is the locus of points at a fixed distance (the radius) from a fixed point (the centre). Every diameter is a line of reflection symmetry, and the circle has rotational symmetry about its centre through any angle.
- Infinitely many circles pass through two given points A and B; all their centres lie on the perpendicular bisector of AB. Through three non-collinear points there is exactly one circle — the circumcircle.
- Equal chords ⇔ equal angles at the centre; equal chords ⇔ equal distances from the centre. The longer of two unequal chords is the nearer one, and the diameter is the longest chord of all.
- The line from the centre to the midpoint of a chord is perpendicular to it, and the perpendicular from the centre bisects the chord. This gives the workhorse formula chord = 2√(r² − d²).
- An arc subtends at the centre twice the angle it subtends at any point of the circle outside the arc. Hence the angle in a semicircle is 90°, and all angles in the same segment are equal.
- Four points are concyclic when a segment subtends equal angles at two points on the same side of it. In a cyclic quadrilateral each pair of opposite angles adds to 180°, and the converse is also true.
Quick revision – I’m Up and Down, and Round and Round
| Result | What it says | Reason in one line | Where you use it |
|---|---|---|---|
| Theorem 1 | Exactly one circle passes through three non-collinear points | The perpendicular bisectors of AB and AC meet at exactly one point | Drawing a circumcircle |
| Theorems 2 & 3 | Equal chords ⇔ equal angles at the centre | SSS (and SAS) on the two radius–chord triangles | Comparing two chords |
| Theorems 4 & 5 | Centre → midpoint of a chord is ⊥ to it; ⊥ from the centre bisects the chord | ΔCMA ≅ ΔCMB, and ∠CMA + ∠CMB = 180° | Splitting a chord in half |
| Theorems 6 & 7 | Equal chords ⇔ equidistant from the centre | RHS on ΔCEA and ΔCHF (half-chords equal, radii equal) | Parallel-chord problems |
| Theorem 8 | Of two unequal chords the longer is nearer the centre | R² = d² + (half-chord)², so d shrinks as the chord grows | Ordering chords by distance |
| Chord formula | Chord = 2√(r² − d²) | Baudhāyana–Pythagoras in the half-chord right triangle | Almost every numerical question |
| Theorem 9 | Angle at the centre = 2 × angle at a point of the circle outside the arc | Exterior-angle theorem applied to two isosceles triangles | Finding unknown angles |
| Corollary | The angle in a semicircle is 90° | Half of the straight angle 180° subtended by a diameter | Spotting right angles in a circle |
| Theorem 10 | Equal angles at two points on the same side of AB ⇒ all four points concyclic | D inside or outside the circle both give a contradiction | Proving points concyclic |
| Theorems 11 & 12 | Opposite angles of a cyclic 4-gon add to 180° (and the converse) | The two halves add to ½ of the complete angle 360° | Cyclic quadrilateral angle chases |
Old NCERT vs New – Class 9 Maths
This chapter is from Ganita Manjari, the new NCERT Class 9 Maths book (NCF-SE 2023, used from 2026-27). It replaced the old book “Mathematics”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Ganita Manjari:
I’m Up and Down, and Round and Round – Overview
| Class | Class 9 |
| Subject | Maths |
| Book | Ganita Manjari – new NCERT book |
| Part | Part I |
| Chapter | 5 of 14 – I’m Up and Down, and Round and Round |
| Book pages | 92 – 117 |
| Edition | Latest NCERT edition (2026-27) |
| Session | 2026-27 |
| Free – read online or download |
Class 9 Maths Chapter 5 – FAQs
Where can I download I’m Up and Down, and Round and Round Class 9 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 9 Maths Chapter 5 about?
A circle is the locus of points at a fixed distance (the radius) from a fixed point (the centre). Every diameter is a line of reflection symmetry, and the circle has rotational symmetry about its centre through any angle.
Is I’m Up and Down, and Round and Round from the new NCERT Class 9 Maths book?
Yes. It is chapter 5 of ganita manjari (part i), the new NCERT Class 9 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 9 Maths Chapter 5?
Open the NCERT Solutions link above for answers to the exercise questions.