CIRCUMCIRCLE

1. TEACHING MANUAL
Name of the teacher : Nimmy Herrycal
Name of the school : Govt.H.S.Vazhamuttom Date :
Subject : Mathematics Duration : 45 minutes
Standard : IX Period :
Unit : Circles Strength :
Topic : Circumcircle
Content Outline
Circles – Circumcircle
Curricular statement : The pupil understandthe conceptof circumcircle.
Learning Outcome : Enable the studentsin
(1) locatingknowledge basedoncircle inlongtermmemory.
(2) constructinga circumcircle.
Content Knowledge
Term : Circumcircle
Facts : (1) A circle isa closedfigure withcentre andradius.
(2) A circumcircle isthe circle passingthroughthe verticesof a triangle.
Concept : Circumcircle
Pre-requisites : The pupil knowsabout
(1) Circle
(2) Chord of a circle
(3) Circle throughtwopoints
Teaching Aids : (1) Activitycardcontainingproblembasedoncircumcircle.

2. (2) Chart containingthe conceptcircumcircle of the triangle.
Reference : MathematicsstandardIX , Part I , Govt of Kerala.
ClassroomInteraction Procedure Pupil Response
Introduction
Tr: We sartedthe lessonbydrawingcircle throughone specificpoint
and the throughtwo specificpoints.How manycirclescanwe drawn
throughthree specificpoints?
Tr; If the pointare on a straightline asbelow ,thenisit possible to
draw a circle throughthem?
Tr:What if theyare not onthe same line?
Presentation
Step: 1 Tr: Firstdraw a triangle ABC

3. Step: 2
Tr : Findthe bisectorof the one of the triangle side .Anyone will do.
See constructingthe perpendicularbisectorof aline segment.
Step: 3
Tr : Repeatforthe otherside . Anyone will do.
Optional step:Repeatforthe thirdside.Thiswill convince youthatthe
three bisectorsdo, infact , intersectata single point.Buttwoare
enoughtofindthat point.
ClassroomInteraction Procedure Pupil Response

4. Step: 4
Tr : The pointwhere these twoperpendicularsintersectisthe
Triangle’scircumcentre , the centre of the circle we desire.
Note : The pointmay lie outside the triangle.Thisisnormal.
Step: 5
Tr : Place the compasses'pointonthe intersectionof the perpendiculars
and setthe compasses'widthtoone of the pointsA,Bor C.Draw a circle
that will passthroughall three.
Step: 5
Tr : Done.The circle drawnis the triangle'scircumcircle,the onlycircle
that will passthroughall three of itsvertices.
ClassroomInteraction Procedure Pupil Response

5. Generalisation
Teachergeneralizesthe conceptusing chart.
ClassroomInteraction Procedure Pupil Response
CIRCUMCIRCLE
A circle which passes through three
vertices of a triangle is called
circumcircle of a triangle

6. ClassroomInteraction Procedure Pupil Response
Application
Teacherdividedthe studentsintogroupsanddistributedactivitycards.
Activity:1
Tr : Draw a triangle withsidesAB= 4cm , BC = 5cm andAC = 6cm .
Thendraw the perpendicularbisector.Take the pointat whichthe
Bisectorintersectasthe centre and draw a circle passingthrough
A , B and C withthe helpof a compass.
Activity:2
Tr : Draw a triangle ABCwithmeasurementsasgivenbelowand
Draw the circumcircle.
AB = 4cm , AC = 5cm and <A =60
Review
(1) Can we drawcirclesthroughthree points?
(2) Define circumcircle.

7. FollowUp Activities
(1) Draw a triangle ABCwithmeasurementsasgivenbelow anddraw the circumcircle of each.
(i) AB = 4cm ; AC = 5cm ; <A =120 .
(ii) AB= 4cm ; AC= 5cm ; <A = 90 .