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

=Activity - Perpendicular bisector of a chord passes through the center of a circle=

Estimated Time
20 minutes

Materials/ Resources needed
Laptop, Geogebra file, projector and a pointer.

Prerequisites/Instructions, if any

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

Website interactives/ links/ simulations
This geogebra has been created by ITfc-Edu-team. <ggb_applet width="1280" height="572" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />

Process (How to do the activity)

 * 1) Show the children the geogebra file and ask the listed questions below.

Developmental Questions (What discussion questions)

 * 1) What is a chord ?
 * 2) At how many points on the circumference does the chord touch a circle.
 * 3) What is a bisector ?
 * 4) What is a perpendicular bisector ?
 * 5) In each case the perpendicular bisector passes through which point ?

Evaluation (Questions for assessment of the child)

 * 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.

Question Corner

 * 1) What do you infer ?
 * 2) How can you reason that the perpendicular bisector for any length of chord always passes through the centre of the circle.

Activity Keywords

 * 1) Geogebra
 * 2) Perpendicular bisector
 * 3) Chord

Back