NCERT Solutions for Class 9th Maths Chapter 5 I’m Up and Down, and Round and Round
Updated on 2026-09-08
About this chapter
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
- Chapter opening
- Definitions
- Symmetries of a Circle
- How Many Circles?
- Chords and the Angles They Subtend
- Midpoints and Perpendicular Bisectors of Chords
- Distance of Chords from the Centre
- Which of the two unequal chords is farther from the centre?
- Angles Subtended by an Arc
- Concyclicity of Points
Exercises
- Chapter opening — In-text Questions Page 92–93
- Definitions — Think and Reflect Page 93
- Think and Reflect — Symmetries of a Circle Page 94
- Think and Reflect — How Many Circles? Page 95
- In-text Questions — How Many Circles? Page 96
- Exercise Set 5.1 — How Many Circles? Page 98
- Think, Draw and Infer — How Many Circles? Page 98
- Exercise Set 5.2 — Chords and the Angles They Subtend Page 100
- Exercise Set 5.3 — Midpoints and Perpendicular Bisectors of Chords Page 101
- In-text Questions — Distance of Chords from the Centre Page 102
- Exercise Set 5.4 — Distance of Chords from the Centre Page 104
- In-text Questions — Which of the two unequal chords is farther from the centre? Page 104
- Exercise Set 5.5 — Which of the two unequal chords is farther from the centre? Page 105–106
- In-text Questions — Angles Subtended by an Arc Page 107
- Exercise Set 5.6 — Angle subtended by an arc at a point on the circle outside the arc Page 110–111
- In-text Questions — Concyclicity of Points Page 113
- Whole chapter — End-of-Chapter Exercises Page 114–116