# Perpendicular bisector of a chord passes through the center of a circle

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Since every perpendicular bisector passes through the centre, the centre must lie on every one of them, so the centre must be their single common point.

### Objectives

- Meaning of circle and chord.
- Method to measure the perpendicular distance of the chord from the centre of the circle.
- Properties of chord.
- Able to relate chord properties to find unknown measures in a circle.
- Apply chord properties for proof of further theorems in circles.

### Estimated Time

20 minutes

### Prerequisites/Instructions, prior preparations, if any

Basic concepts of a circle and its related terms should have been covered.

### Materials/ Resources needed

Digital: Laptop, Geogebra file, projector and a pointer.

Geogebra file: Chord and perpendicular bisector.gg

Download this geogebra file from this link.

### Process (How to do the activity)

Show the children the geogebra file and ask the listed questions below.

- What is a chord ?
- At how many points on the circumference does the chord touch a circle .
- What is a bisector ?
- What is a perpendicular bisector ?
- In each case the perpendicular bisector passes through which point ?

**Evaluation**

- What is the angle formed at the point of intersection of chord and radius ?
- Are the students able to understand what a perpendicular bisector is ?
- Are the students realising that perpendicular bisector drawn for any length of chords for any circle always passes through the center of the circle .
- What do you infer ?
- How can you reason that the perpendicular bisector for any length of chord always passes through the centre of the circle.