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

Concept #1 CHORD

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

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• Estimated Time
  

20 minutes

• Materials/ Resources needed:

Laptop, Geogebra file, projector and a pointer.

• 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 #

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

Concept #2.SECANT

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Activity No #

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• Evaluation
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Concept #3.TANGENT

Activity No #

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Activity No #

Click to Comment

• 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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