NCERT Ganita Manjari, Class 9, textbook pages 92–117 (Part I)

How to help your child with Class 9 Maths Chapter 5, I’m Up and Down, and Round and Round, at home

Circles: chords, arcs and angles, explained for parents: a 30-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

perpendicular bisects the chordchordradius

NCERT Class 9 Maths Chapter 5 I’m Up and Down, and Round and Round: what it teaches

Your teen studies circles: radius, chord, arc, the symmetry of a circle, perpendicular from the centre bisecting a chord, equal chords equidistant from the centre, angles subtended by arcs, and when points lie on one circle (concyclic).

Why it matters later. Circle theorems continue in Class 10 (tangents) and are used in coordinate geometry.

See it: this chapter in pictures

2θθangle at centre = 2 × angle on circle
The centre angle is double.
equal chords, equal distance from centre
Equal chords are equally far from the centre.
centre of a plate?draw 2 chordsbisectors meet at the centre
A practical use of chord properties.

You need

  • compass, ruler, protractor
  • paper circles for folding
  • a round plate

Tonight’s 30 minutes

  1. Fold a paper circle: every fold through the centre is a line of symmetry.
  2. Draw a chord and the perpendicular from the centre. Measure both halves.
  3. Draw an arc and angles it subtends at the centre and on the circle. Compare (centre angle is double).
  4. Find the centre of a plate by drawing two chords and their perpendicular bisectors.

Words to use

  • radius
  • chord
  • arc
  • subtend
  • perpendicular bisector
  • concyclic

Watch for

  • Confusing chord and arc. A chord is a straight segment; an arc is part of the circle.
  • Measuring the angle at the wrong point. Mark which point the angle is at before measuring.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouHow can we find the centre of this plate?

Your childDraw two chords and their perpendicular bisectors.

A game for this week: Find the centre

  1. Give a paper circle with its centre hidden.
  2. Construct the centre with two chords.
  3. Check with a pin.
  4. Closest wins.

A 5-day plan, 30 minutes a day

  1. Day 1Folding symmetry.
  2. Day 2Chord bisector.
  3. Day 3Angles by arcs.
  4. Day 4Find a plate’s centre.
  5. Day 5Find the centre game.

Everyday moments to practise

  • Wheels and gears.
  • Clock faces.
  • Circular tracks.
  • Arches and domes.

Quick check

Ask these at the end of the week. Tap to see the answer.

Does the perpendicular from the centre bisect a chord?

Yes.

Angle at centre is 100°. Angle on the circle for the same arc?

50°.

How do you find a circle’s centre?

Intersect perpendicular bisectors of two chords.

Ready for the next chapter when your child…

  • Uses chord properties.
  • Knows angle at centre is double.
  • Constructs a circle’s centre.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Manjari (Class 9). See the full Class 9 parent guide for every chapter.

Questions parents ask

What is a chord?

A line segment joining two points on a circle.

What is the angle at the centre theorem?

The angle an arc makes at the centre is twice the angle it makes on the circle.

What are concyclic points?

Points that lie on the same circle.