The longest chord passes through the centre of the circle

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=Additional Information=

Useful websites

 * 1) www.regentsprep.com conatins good objective problems on chords and secants
 * 2) www.mathwarehouse.com contains good content on circles for different classes
 * 3) staff.argyll contains good simulations

Reference Books
= Teaching Outlines Chord and its related theorems

Learning objectives
The students should be able to:
 * 1) Recall the meaning of circle and chord.
 * 2) State Properties of chord.
 * 3) By studying the theorems related to chords, the students should know that a chord in a circle is an important concept.
 * 4) They should be able to relate chord properties to find unknown measures in a circle.
 * 5) They should be able to apply chord properties for proof of further theorems in circles.

Notes for teachers
A chord is a straight line joining 2 points on the circumference of a circle. Chords within a circle can be related many ways. The theorems that involve chords of a circle are : Perpendicular bisector of a chord passes through the center of a circle. Congruent chords are equidistant from the center of a circle. If two chords in a circle are congruent, then their intercepted arcs are congruent. If two chords in a circle are congruent, then they determine two central angles that are congruent.

Activity No 1 Theorem 1: Perpendicular bisector of a chord passes through the center of a circle.
20 minutes Laptop, Geogebra file, projector and a pointer.
 * Estimated Time
 * Materials/ Resources needed:
 * Prerequisites/Instructions, if any
 * 1) The students should know the basic concepts of a circle and its related terms.
 * 2) They should have prior knowledge of chord and construction of perpendicular bisector to the chord.
 * Multimedia resources: Laptop


 * Website interactives/ links/ / Geogebra Applets


 * Process:
 * 1) Show the children the geogebra file.
 * 2) Let them identify the chord. Ask them to define a chord.
 * 3) perpendicular bisector.
 * 4) Show them the 2nd chord.
 * 5) Let students observe if everytime the perpendicular bisector of the chord passes through the centre of the circle.
 * Developmental 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 ?
 * 6) Can anyone explain why does the perpendicular bisector always passes through the centre of the circle ?


 * 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.
 * 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 No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

Activity No #

 * Estimated Time
 * Materials/ Resources needed
 * Prerequisites/Instructions, if any
 * Multimedia resources
 * Website interactives/ links/ / Geogebra Applets
 * Process/ Developmental Questions
 * Evaluation
 * Question Corner

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