Difference between revisions of "The longest chord passes through the centre of the circle"

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==Reference Books==
 
==Reference Books==
  
−
= Teaching Outlines =
+
= Teaching Outlines  
−
 
+
Chord and its related theorems
 
==Concept #1 CHORD==
 
==Concept #1 CHORD==
 
===Learning objectives===
 
===Learning objectives===
 
The students should be able to:<br>
 
The students should be able to:<br>
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*Recall the meaning of circle.<br>
+
#Recall the meaning of circle and chord.<br>
−
*Define chord.<br>
+
#State Properties of chord.<br>
−
*State Properties of chord.<br>
+
# By studying the theorems related to chords, the students should know that a chord in a circle is an important concept .
 +
# They should be able to relate chord properties to find unknown measures in a circle.
 +
# They should be able to apply chord properties for proof of further theorems in circles.
  
 
===Notes for teachers===
 
===Notes for teachers===
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The teacher should clarify the meaning of chord and circle to the students
+
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 Construction of chord  ===
+
===Activity No 1   ===
 
{| style="height:10px; float:right; align:center;"
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
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|}
 
|}
 
*Estimated Time <br>
 
*Estimated Time <br>
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10-15 minutes
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20 minutes
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*Materials/ Resources needed
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*Materials/ Resources needed:
−
#circular paper cuttings
+
Laptop, Geogebra file, projector and a pointer.
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#sketch pen
 
−
#note book
 
−
#pen
 
 
*Prerequisites/Instructions, if any
 
*Prerequisites/Instructions, if any
−
#Meaning of chord.
+
# The students should know the basic concepts of a circle and its related terms.
−
#Meaning of circle.
+
# They should have prior knowledge of chord and construction of perpendicular bisector to the chord.
−
#Meaning of circumference
+
*Multimedia resources: Laptop
−
*Multimedia resources
 
  
 
*Website interactives/ links/ / Geogebra Applets
 
*Website interactives/ links/ / Geogebra Applets
  
−
*Process/ Developmental Questions
+
*Process:
−
#what is a chord?
+
# Show the children the geogebra file.
−
#The folded line connected from where to where?
+
# Let them identify the chord. Ask them to define a chord.
−
#How many chords can be drawn in a circle?
+
# perpendicular bisector.
 +
# Show them the 2nd chord.
 +
# Let students observe if everytime the perpendicular bisector of the chord passes through the centre of the circle.
 +
*Developmental Questions:
 +
# 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 ?
 +
# Can anyone explain why does the perpendicular bisector always passes through the centre of the circle ?
 +
 
 
*Evaluation
 
*Evaluation
−
#was the effect of chord in a circle?
+
# What is the angle formed at the point of intersection of chord and radius ?
−
#Was the student able to give the meaning of chord?
+
# 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 .
−
*Question Corner
+
*Question Corner:
−
#how many chords can be drawn in a circle?
+
# What do you infer ?
−
#What happens to the size of the chord if it moves away from the centre?
+
# How can you reason that the perpendicular bisector for any length of chord always passes through the centre of the circle.
−
#If the chord pass through the centre of the circle what it are the properties of that chord?
 
  
 
===Activity No # ===
 
===Activity No # ===

Revision as of 10:15, 3 November 2013

The Story of Mathematics

Philosophy of Mathematics

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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

  • 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 #

  • 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

Learning objectives

Notes for teachers

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

Concept #3.TANGENT

Learning objectives

Notes for teachers

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

Hints for difficult problems

Project Ideas

Math Fun

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