Class 9 Mathematics Chapter 5 I’m Up and Down, and Round and Round – Revision Notes

Quick revision notes for Class 9 Maths Chapter 5 (I’m Up and Down, and Round and Round — Circles). These Class 9 Mathematics Chapter 5 notes are ideal for quick revision just before exams.

Basic Terms

• Radius: centre to circle. Chord: joins 2 points on circle. Diameter: longest chord (through centre).

Chord Properties

• Equal chords → equal angles at centre.
• Perpendicular from centre bisects chord (and vice versa).
• Perpendicular bisector of any chord passes through centre.

Angles

• Angle at centre = 2 × angle at circumference (same arc).
• Angle in semicircle = 90°.

Circumcircle

• Circumcentre: intersection of perpendicular bisectors of triangle’s sides.

Cyclic Quadrilaterals

• Opposite angles supplementary (sum 180°).
• Exterior angle = opposite interior angle.

One-Line Summary

Circle geometry connects chords, arcs, and angles — equal chords give equal central angles, a diameter always subtends 90°, and cyclic quadrilaterals always have supplementary opposite angles.

Written by Satish

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