Difference between revisions of "Circles Constructions"

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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
 
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[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
 
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
 
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
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= Concept Map =
 
= Concept Map =
 
__FORCETOC__
 
__FORCETOC__
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<mm>[[Circles_Constructions.mm|flash]]</mm>
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[[File:Circles_Constructions.mm|flash]]
  
 
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*Estimated Time
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*Materials/ Resources needed
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*Prerequisites/Instructions, if any
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*Multimedia resources
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*Website interactives/ links/ / Geogebra Applets
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*Process/ Developmental Questions
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*Evaluation
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*Question Corner
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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*Estimated Time
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*Materials/ Resources needed
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*Prerequisites/Instructions, if any
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*Multimedia resources
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*Website interactives/ links/ / Geogebra Applets
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*Process/ Developmental Questions
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*Evaluation
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*Question Corner
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===Activity No # ===
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*Estimated Time
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*Materials/ Resources needed
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*Prerequisites/Instructions, if any
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*Multimedia resources
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*Website interactives/ links/ / Geogebra Applets
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*Process/ Developmental Questions
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*Evaluation
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*Question Corner
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===Activity No # ===
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{| style="height:10px; float:right; align:center;"
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*Estimated Time
 
*Estimated Time
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*Evaluation
 
*Evaluation
 
*Question Corner
 
*Question Corner
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===Activity No # Construct a direct common tangent to two circles with given radii and given distance between the centre of two circles.===
 +
{| style="height:10px; float:right; align:center;"
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|<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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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
 +
*Estimated Time: 90 minutes
 +
*Materials/ Resources needed: # Laptop, geogebra file, projector and a pointer.
 +
# Students' individual construction materials.
 +
*Prerequisites/Instructions, if any:
 +
# The students should have prior knowledge of a circle , tangent and the limiting case of a
 +
secant as a tangent.
 +
# They should understand that a tangent is always perpendicular to the radius of the circle.
 +
# They should know construction of a tangent to a given point.
 +
# If the same straight line is a tangent to two or more circles, then it is called a common tangent.
 +
# If the centres of the circles lie on the same side of the common tangent, then the tangent is called a direct common tangent.
 +
# Note: In general,
 +
*The two circles are named as C1 and C2
 +
* The distance between the centre of two circles is 'd'
 +
* Radius of one circle is taken as 'R' and other as 'r'
 +
* The length of tangent is 't'
 +
*Multimedia resources: Laptop
 +
*Website interactives/ links/ / Geogebra Applets
 +
*Process:
 +
[Note for  teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]<br>
 +
The teacher can explain the step by step construction of Direct common tangent  and with an example
 +
*Developmental Questions:
 +
# What is a tangent
 +
# What is a common tangent ?
 +
# What is a direct common tangent ?
 +
# What is R and r  ?
 +
# What does the length OA represent here ?
 +
# Why was a third circle constructed ?
 +
# Let us try to construct direct common tangent without the third circle and see.
 +
# What should be the radius of the third circle ?
 +
# Why was OA bisected and semi circle constructed ?
 +
# What were OB and OC extended ?
 +
# What can you say about lines AB and AC ?
 +
# Name the direct common tangents .
 +
# At what points is the tangent touching the circles ?
 +
# Identify the two right angled triangles formed from the figure ? What do you understand ?
 +
*Evaluation:
 +
# Is the student able to comprehend the sequence of steps in constructing the tangent.
 +
# Is the student able to identify error areas while constructing ?
 +
# Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
 +
# Is the student able to appreciate that the direct common tangents from the same external point are equal and subtend equal angles at the center.
 +
*Question Corner:
 +
# What do you think are the applications of tangent constructions ?
 +
# What is the formula to find the length of direct common tangent ?
 +
# Can a direct common tangent be drawn to two circles one inside the other ? 
 +
# Observe the point of intersection of extended tangents in relation with the centres of two circles. Infer.
 +
# What are properties of direct common tangents ?
 +
 
===Activity No # ===
 
===Activity No # ===
 
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*Estimated Time
 
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*Evaluation
 
*Evaluation
 
*Question Corner
 
*Question Corner
 +
 
===Activity No # ===
 
===Activity No # ===
 
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*Evaluation
 
*Evaluation
 
*Question Corner
 
*Question Corner
 +
 +
==Concept #4. Construction of transverse common tangent.==
 +
===Learning objectives===
 +
===Notes for teachers===
 +
===Activity No # ===
 +
{| style="height:10px; float:right; align:center;"
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|<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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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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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
 +
===Activity No # ===
 +
{| style="height:10px; float:right; align:center;"
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|<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;">
 +
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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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
 +
===Activity No # ===
 +
{| style="height:10px; float:right; align:center;"
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|<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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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
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*Estimated Time
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*Materials/ Resources needed
 +
*Prerequisites/Instructions, if any
 +
*Multimedia resources
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*Website interactives/ links/ / Geogebra Applets
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*Process/ Developmental Questions
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*Evaluation
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*Question Corner
 +
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===Activity No # ===
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{| style="height:10px; float:right; align:center;"
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|<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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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
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*Estimated Time
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*Materials/ Resources needed
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*Prerequisites/Instructions, if any
 +
*Multimedia resources
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*Website interactives/ links/ / Geogebra Applets
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*Process/ Developmental Questions
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*Evaluation
 +
*Question Corner
 +
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===Activity No # ===
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{| style="height:10px; float:right; align:center;"
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
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*Estimated Time
 +
*Materials/ Resources needed
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*Prerequisites/Instructions, if any
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*Multimedia resources
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*Website interactives/ links/ / Geogebra Applets
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*Process/ Developmental Questions
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*Evaluation
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*Question Corner
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= Hints for difficult problems =
 
= Hints for difficult problems =
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Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 +
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[[Category:Circles]]

Latest revision as of 16:30, 29 October 2019

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.

Concept Map

[maximize]

Textbook

To add textbook links, please follow these instructions to: (Click to create the subpage)

Additional Information

Useful websites

Reference Books

Teaching Outlines

Concept #1. Construction of chord.

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 #2. Construction of 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

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. Construction of direct common 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

Activity No # Construct a direct common tangent to two circles with given radii and given distance between the centre of two circles.

  • Estimated Time: 90 minutes
  • Materials/ Resources needed: # Laptop, geogebra file, projector and a pointer.
  1. Students' individual construction materials.
  • Prerequisites/Instructions, if any:
  1. The students should have prior knowledge of a circle , tangent and the limiting case of a

secant as a tangent.

  1. They should understand that a tangent is always perpendicular to the radius of the circle.
  2. They should know construction of a tangent to a given point.
  3. If the same straight line is a tangent to two or more circles, then it is called a common tangent.
  4. If the centres of the circles lie on the same side of the common tangent, then the tangent is called a direct common tangent.
  5. Note: In general,
  • The two circles are named as C1 and C2
  • The distance between the centre of two circles is 'd'
  • Radius of one circle is taken as 'R' and other as 'r'
  • The length of tangent is 't'
  • Multimedia resources: Laptop
  • Website interactives/ links/ / Geogebra Applets
  • Process:

[Note for teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]
The teacher can explain the step by step construction of Direct common tangent and with an example

  • Developmental Questions:
  1. What is a tangent
  2. What is a common tangent ?
  3. What is a direct common tangent ?
  4. What is R and r ?
  5. What does the length OA represent here ?
  6. Why was a third circle constructed ?
  7. Let us try to construct direct common tangent without the third circle and see.
  8. What should be the radius of the third circle ?
  9. Why was OA bisected and semi circle constructed ?
  10. What were OB and OC extended ?
  11. What can you say about lines AB and AC ?
  12. Name the direct common tangents .
  13. At what points is the tangent touching the circles ?
  14. Identify the two right angled triangles formed from the figure ? What do you understand ?
  • Evaluation:
  1. Is the student able to comprehend the sequence of steps in constructing the tangent.
  2. Is the student able to identify error areas while constructing ?
  3. Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
  4. Is the student able to appreciate that the direct common tangents from the same external point are equal and subtend equal angles at the center.
  • Question Corner:
  1. What do you think are the applications of tangent constructions ?
  2. What is the formula to find the length of direct common tangent ?
  3. Can a direct common tangent be drawn to two circles one inside the other ?
  4. Observe the point of intersection of extended tangents in relation with the centres of two circles. Infer.
  5. What are properties of direct common tangents ?

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Concept #4. Construction of transverse common tangent.

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