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

This chapter on circles starts from basic terms like radius and chord before building up to angle relationships — including why opposite angles in a cyclic quadrilateral always add up to 180 degrees.

Last Updated: September 23, 2026

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.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

What information does a linear equation in two variables represent graphically?
A linear equation in two variables represents a straight line when plotted on a Cartesian plane, and every point on that line corresponds to an ordered pair of values that satisfies the equation.

How many solutions does a linear equation in two variables have?
A linear equation in two variables has infinitely many solutions, since for every value chosen for one variable, a corresponding value of the other variable can be found that satisfies the equation.

Written by Satish

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