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From Karnataka Open Educational Resources
The longest chord passes through the centre of the circle (view source)
Revision as of 10:15, 3 November 2013
, 10:15, 3 November 2013no edit summary
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+*Recall the meaning of circle.<br>+*Define chord.<br>+*State Properties of chord.<br>+10-15 minutes+#circular paper cuttings+#sketch pen
−#note book
−#pen
#Meaning of circumference+
+#If the chord pass through the centre of the circle what it are the properties of that chord?
==Reference Books==
==Reference Books==
−= Teaching Outlines =
+= Teaching Outlines
−Chord and its related theorems
==Concept #1 CHORD==
==Concept #1 CHORD==
===Learning objectives===
===Learning objectives===
The students should be able to:<br>
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===
===Notes for teachers===
−The teacher should clarify the meaning of chord and circle to the students
+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 Construction of chord ===
+===Activity No 1 ===
{| 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;">
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|}
|}
*Estimated Time <br>
*Estimated Time <br>
−20 minutes
−*Materials/ Resources needed
+*Materials/ Resources needed:
−Laptop, Geogebra file, projector and a pointer.
−*Prerequisites/Instructions, if any
*Prerequisites/Instructions, if any
−#Meaning of chord.
+# The students should know the basic concepts of a circle and its related terms.
−#Meaning of circle.
+# They should have prior knowledge of chord and construction of perpendicular bisector to the chord.
−*Multimedia resources: Laptop
−*Multimedia resources
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets
−*Process/ Developmental Questions
+*Process:
−#what is a chord?
+# Show the children the geogebra file.
−#The folded line connected from where to where?
+# Let them identify the chord. Ask them to define a chord.
−#How many chords can be drawn in a circle?
+# perpendicular bisector.
+# Show them the 2nd 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
*Evaluation
−#was the effect of chord in a circle?
+# What is the angle formed at the point of intersection of chord and radius ?
−#Was the student able to give the meaning of chord?
+# 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
+*Question Corner:
−#how many chords can be drawn in a circle?
+# What do you infer ?
−#What happens to the size of the chord if it moves away from the centre?
+# How can you reason that the perpendicular bisector for any length of chord always passes through the centre of the circle.
−===Activity No # ===
===Activity No # ===
