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From Karnataka Open Educational Resources
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added Category:Circles using HotCat
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<mm>[[Circles_Constructions.mm|flash]]</mm>+ +
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−[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
+[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
−|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]
+|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]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
|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:_Pedagogy Teaching of Mathematics]
+[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
|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/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
+[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
|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:_Topics Topics in School Mathematics]
+[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
|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/Text_Books#Mathematics_-_Textbooks Textbooks]
+[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
|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/Maths:_Question_Papers Question Bank]
+[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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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__
−[[File:Circles_Constructions.mm|flash]]
= Textbook =
= Textbook =
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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://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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{| style="height:10px; float:right; align:center;"
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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{| style="height:10px; float:right; align:center;"
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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*Evaluation
*Evaluation
*Question Corner
*Question Corner
−===Activity No # ===
+===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;"
{| 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;">
−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−*Estimated Time
+*Estimated Time: 90 minutes
−*Materials/ Resources needed
+*Materials/ Resources needed: # Laptop, geogebra file, projector and a pointer.
−*Prerequisites/Instructions, if any
+# Students' individual construction materials.
−*Multimedia resources
+*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
*Website interactives/ links/ / Geogebra Applets
−*Process/ Developmental Questions
+*Process:
−*Evaluation
+[Note for teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]<br>
−*Question Corner
+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 # ===
{| style="height:10px; float:right; align:center;"
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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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://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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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://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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−''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
+''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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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
+
+[[Category:Circles]]
