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

Latest revision as of 16:17, 4 November 2019

Investigating the diameter is the longest chord of a circle.

Objectives

To understand longest chord passes through the centre and it is the diameter

Estimated Time

30 minutes

Prerequisites/Instructions, prior preparations, if any

Prior knowledge of point, lines, angles, polygons

Materials/ Resources needed

Digital : Computer, geogebra application, projector.
Non digital : Worksheet and pencil, compass, strings
Geogebra files : Diameter is longest chord.ggb

Download this geogebra file from this link.

Process (How to do the activity)

Use the geogebra file to show how diameter is the longest chord.

Move the points on the circle to show the changes in the triangle.

What is the condition with respect to sides for formation of a triangle. Sum of two sides is larger than the third side.

Compare the chord length with sum of two radii. When is the triangle reduced to a line segment.

What can you conclude about the chord? When is it the largest?

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+Investigating the diameter is the longest chord of a circle.
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-[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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-[http://www.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'''].
-= Concept Map =
+===Objectives===
-__FORCETOC__
+To understand longest chord passes through the centre and it is the diameter
-= Textbook =
+===Estimated Time===
-To add textbook links, please follow these instructions to:
+minutes
-([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
-=Additional Information=
+===Prerequisites/Instructions, prior preparations, if any===
-==Useful websites==
+Prior knowledge of point, lines, angles, polygons
-#[http://www.regentsprep.org/Regents/math/geometry/GP14/PracCircleSegments.htm www.regentsprep.com] conatins good objective problems on chords and secants <br>
-#[http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php www.mathwarehouse.com] contains good content on circles for different classes<br>
-#[http://staff.argyll.epsb.ca/jreed/math20p/circles/tangent.htm staff.argyll]  contains good simulations
-==Reference Books==
+===Materials/ Resources needed===
+* Digital : Computer, geogebra application, projector.
+* Non digital : Worksheet and pencil, compass, strings
+* Geogebra files :  [https://ggbm.at/c4eg7q2u Diameter is longest chord.ggb]
+{{Geogebra|c4eg7q2u}}
-= Teaching Outlines =
+===Process (How to do the activity)===
+Use the geogebra file to show how diameter is the longest chord.
-==Concept #1 construction of chords==
+Move the points on the circle to show the changes in the triangle.
-===Learning objectives===
-The students should be able to:<br>
-*Recall the meaning of circle.<br>
-*Define chord.<br>
-*State Properties of chord.<br>
-*Construct chord of given size.
-===Notes for teachers===
+What is the condition with respect to sides for formation of a triangle. Sum of two sides is larger than the third side.
-The teacher should clarify the meaning of chord and circle to the students
-===Activity No # ===
+Compare the chord length with sum of two radii. When is the triangle reduced to a line segment.
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-''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
-|}
-*Estimated Time
-*Materials/ Resources needed
-*Prerequisites/Instructions, if any
-*Multimedia resources
-*Website interactives/ links/ / Geogebra Applets
-*Process/ Developmental Questions
-*Evaluation
-*Question Corner
-===Activity No # ===
+What can you conclude about the chord? When is it the largest?
-{| 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;">
-''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
-|}
-*Estimated Time
-*Materials/ Resources needed
-*Prerequisites/Instructions, if any
-*Multimedia resources
-*Website interactives/ links/ / Geogebra Applets
-*Process/ Developmental Questions
-*Evaluation
-*Question Corner
-==Concept #==
+[[Category:Circles]]
-===Learning objectives===
-===Notes for teachers===
-===Activity No # ===
-{| 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;">
-''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
-|}
-*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;"
-|<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>
-|}
-*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 =
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