NCERT Solutions Class 9 Maths Chapter 5 — I’m Up and Down, and Round and Round#

Chapter 5 studies patterns of change — quantities that rise and fall, and motions that repeat in cycles. You will learn to describe and analyse such variation, spot symmetry and periodicity, and represent these behaviours mathematically.

Exercises#

• Exercise Set 5.1 — Drawing circumcircles, circumcentre inside or outside, least circle through two points (4 questions)
• Exercise Set 5.2 — The isosceles triangle formed by a chord and the centre (2 questions)
• Exercise Set 5.3 — The perpendicular from the centre bisects a chord, distance between parallel chords (3 questions)
• Exercise Set 5.4 — Equal chords and their distances from the centre (3 questions)
• Exercise Set 5.5 — Chord length $2\sqrt{r^2 - d^2}$ (3 questions)
• Exercise Set 5.6 — Angles subtended by arcs, angles in the same segment (3 questions)
• End-of-Chapter Exercises — Chord lengths, cyclic quadrilaterals, and proofs about chords and circles (26 questions)

What you will learn#

• Chords, the centre and the circle through three points (the circumcircle).
• Why the perpendicular from the centre bisects a chord, and why equal chords are equidistant from the centre.
• The length of a chord from the radius and its distance from the centre.
• Angles subtended by arcs, angles in the same segment and cyclic quadrilaterals.

Key formulas and results#

• A chord at distance $d$ from the centre of a circle of radius $r$ has length $2\sqrt{r^2 - d^2}$.
• The angle an arc subtends at the centre is twice the angle it subtends at any point on the rest of the circle.
• Opposite angles of a cyclic quadrilateral add up to 180°.

Read and revise#

• NCERT Class 9 Maths Chapter 5 (PDF) — the Ganita Manjari Part I chapter itself.
• All Class 9 Maths chapters from Ganita Manjari Part I and Part II.

Frequently asked questions#