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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-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===
-<mm>[[circles_and_lines.mm]]</mm>
+To understand longest chord passes through the centre and it is the diameter
-__FORCETOC__
+===Estimated Time===
+minutes
-= Textbook =
+===Prerequisites/Instructions, prior preparations, if any===
-To add textbook links, please follow these instructions to:
+Prior knowledge of point, lines, angles, polygons
-([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
-=Additional Information=
+===Materials/ Resources needed===
-==Useful websites==
+* Digital : Computer, geogebra application, projector.
-#[http://www.regentsprep.org/Regents/math/geometry/GP14/PracCircleSegments.htm www.regentsprep.com] conatins good objective problems on chords and secants <br>
+* Non digital : Worksheet and pencil, compass, strings
-#[http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php www.mathwarehouse.com] contains good content on circles for different classes<br>
+* Geogebra files :  [https://ggbm.at/c4eg7q2u Diameter is longest chord.ggb]
-#[http://staff.argyll.epsb.ca/jreed/math20p/circles/tangent.htm staff.argyll]  contains good simulations
+{{Geogebra|c4eg7q2u}}
-==Reference Books==
+===Process (How to do the activity)===
+Use the geogebra file to show how diameter is the longest chord.
-= Teaching Outlines =
+Move the points on the circle to show the changes in the triangle.
-==Concept #1 CHORD==
+What is the condition with respect to sides for formation of a triangle. Sum of two sides is larger than the third side.
-===Learning objectives===
-The students should be able to:<br>
-*Recall the meaning of circle.<br>
-*Define chord.<br>
-*State Properties of chord.<br>
-===Notes for teachers===
+Compare the chord length with sum of two radii. When is the triangle reduced to a line segment.
-The teacher should clarify the meaning of chord and circle to the students
-===Activity No 1 Construction of chord  ===
+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 <br>
--15 minutes
-*Materials/ Resources needed
-#circular paper cuttings
-#sketch pen
-#note book
-#pen
-*Prerequisites/Instructions, if any
-#Meaning of chord.
-#Meaning of circle.
-#Meaning of circumference
-*Multimedia resources
-*Website interactives/ links/ / Geogebra Applets
+[[Category:Circles]]
-*Process/ Developmental Questions
-#what is a chord?
-#The folded line connected from where to where?
-#How many chords can be drawn in a circle?
-*Evaluation
-#was the effect of chord in a circle?
-#Was the student able to give the meaning of chord?
-*Question Corner
-#how many chords can be drawn in a circle?
-#What happens to the size of the chord if it moves away from the centre?
-#If the chord pass through the centre of the circle  what it are the properties of that chord?
-===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
-==Concept #2.SECANT==
-===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
-==Concept #3.TANGENT==
-===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
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