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08 October, 2007

angle subtended by an arc

Aim By paper cutting and pasting verify that angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any other point on the remaining part of the circle.



Material required
coloured paper, a pair of scissors, geometry box, fevistick, carbon paper.



Procedure
step 1 Draw a circle of any radius with centre O on a coloured paper and cut it.
step 2 Take a rectangular sheet of paper and paste the circle cut out on it.

step 3 Mark two points A and B on the circle to get arc AB.

step 4 Form a crease joining OA and draw OA.

step 5 Form a crease joining OB and draw OB.

step 6 Take a point C on the remaining part of the circle.


step 7 Form a crease joining AC and draw AC.
step 8 Form a crease joining BC and draw BC.

step 9 Make two replicas of angle ACB using carbon paper.


step 10 Place the two replicas of angle ACB adjacent to each other on angle AOB.


Observations
1. Arc AB subtends angle AOB at the centre and angle ACB at the point C on the remaining part of the circle.
2. Two replicas of angle ACB completely cover angle AOB.
Result

angle AOB = 2 (angle ACB)
Thus its is verified that "angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any other point on the remaining part of the circle."

2 comments:

Anonymous said...

Hello! I am Rahul Gupta of class IX-G want to share what I learned in my maths activity class.By doing theorum ''Angle subtended by an arc at the centre is doubled the angle subtended by it on the remaining part of the circle'' by paper cutting and pasting I visualize this easily.It was difficult for me to learn this from my mathematics book as in that I have to learn the theorum and its proof. By doing activity in maths activity class I have learnt all the algabric identities and theorums of circle and parallelogram easily.
Thank You

Anonymous said...

hi!! friends... This is Samridhi Gupta of IX-G!
Today.. I'de like to tell u something..
When i came to class IX , i discovered that studying pattern of maths is totally different from last year! We now have to proof theorems!! It became very difficult and confusing!
Then I tried to study in Maths Lab .. and .. i said to myself.. let me give it a chance at least..
and really friends.. i found this lab awesome! Now, I'm able to understand them in some minutes .. and .. that too creatively but paper cutting n pasting! Even i got to know many things...
I'm really thankful to my school for this..!!

SaMrIdHi GuPta
IX-'G'
32 {RoLl NO.}

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