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

Process (How to do the activity)
Show the children the geogebra file and ask the listed questions below. Evaluation
 * 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 ?
 * 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.