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.
- 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.
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 ?
- 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.