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===
-__FORCETOC__
+To understand longest chord passes through the centre and it is the diameter
-<mm>[[circles_and_lines.mm|flash]]</mm>
+===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.
-Chord and its related theorems
-==Concept #1 CHORD==
-===Learning objectives===
-The students should be able to:<br>
-#Recall the meaning of circle and 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===
+What is the condition with respect to sides for formation of a triangle. Sum of two sides is larger than the third side.
-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 Theorem 1: Perpendicular bisector of a chord passes through the center of a circle. ===
+Compare the chord length with sum of two radii. When is the triangle reduced to a line segment.
-{| 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>
-minutes
-*Materials/ Resources needed:
-Laptop, Geogebra file, projector and a pointer.
-*Prerequisites/Instructions, if any
-# The students should know the basic concepts of a circle and its related terms.
-# They should have prior knowledge of chord and construction of perpendicular bisector to the chord.
-*Multimedia resources: Laptop
-*Website interactives/ links/ / Geogebra Applets
+What can you conclude about the chord? When is it the largest?
-*Process:
+[[Category:Circles]]
-# Show the children the geogebra file.
-# Let them identify the chord. Ask them to define a chord.
-# Let them recall what a perpendicular bisector is.
-# Show them the second 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
-# What is the angle formed at the point of intersection of chord and radius ?
-# 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:
-# What do you infer ?
-# How can you reason that the perpendicular bisector for any length of chord always passes through the centre of the circle.
-===Activity No # 2.Theorem 2.Congruent chords are equidistant from the center of a circle. ===
-{| 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
-= Hints for difficult problems =
-= Project Ideas =
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