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Chord and Its Properties

A chord is a line segment joining two points on a circle. The perpendicular from the centre of a circle to a chord bisects the chord, and equal chords are equidistant from the centre.

Practice This Concept

Main explanation

Teacher explanation

The centre gives strong information about chords. If a radius from the centre meets a chord at 90 degrees, it cuts that chord into two equal parts. Also, if two chords are equal in length, their perpendicular distances from the centre are equal.

Example

If OM is perpendicular to chord AB and M lies on AB, then AM = MB. If chords AB and CD are equal, then their distances from O are equal.

Simple analogy

Perpendicular from centre cuts chord into two equal pieces.

Common confusion

Students often assume any line from the centre to a chord bisects it. The bisecting result needs the line to be perpendicular to the chord.

Exam tip

In proof questions, write both facts: perpendicular from centre to chord and hence it bisects the chord. Do not skip the 90 degree condition.

Study the chord and its properties diagram carefully

Use the labelled diagram to keep chord and its properties clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of chord and its properties in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on chord and its properties.

Revision cue

Revise chord and its properties through the labels before writing the answer.

Answer writing and exam use

1-mark use

Write the exact meaning of chord and its properties in one clean line.

2-mark use

Define chord and its properties and add one example or condition.

3-mark use

Explain chord and its properties, show the method or example, and mention the common mistake.

MCQ Quiz

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