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

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

1. Meaning of circle and chord.
2. Method to measure the perpendicular distance of the chord from the centre of the circle.
3. Properties of chord.
4. Able to relate chord properties to find unknown measures in a circle.
5. 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

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