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C2 radian question

Hey, really stuck on this question I dont even understand the information I'm given. I'll write down the question but if anyone has an edexcel C2 book it is p.84 q.10 as there is a diagram there.

"in the diagram OAB is a sector of a circle, centre O and radius R cm, and <AOB = 2 theta radians. A circle cantre C and radius r cm, touches the arc AB at T, and touches OA & OB at D and E respectively, as shown."
b) using triangle OCE, show that R sin theta = r(1 +sin theta)

Sorry its hard to understand when written out, but if you have the book the diagrams there. Any help would be muchly appreciated.
Thanks
Reply 1
I'll draw out the diagram and try to figure it out....
Reply 2
Cheers man
Reply 3
It's baffled me too. Since the smaller circle touches OA and OB, you can assume that these act as tangents, and so they make 90 degrees with the radius of the smaller circle. You can also assume that since it touches T, that the arc length acts as a tangent, so that makes 90 degrees with the radius of the circle.

What was part a of the question?
jimber
Hey, really stuck on this question I dont even understand the information I'm given. I'll write down the question but if anyone has an edexcel C2 book it is p.84 q.10 as there is a diagram there.

"in the diagram OAB is a sector of a circle, centre O and radius R cm, and <AOB = 2 theta radians. A circle cantre C and radius r cm, touches the arc AB at T, and touches OA & OB at D and E respectively, as shown."
b) using triangle OCE, show that R sin theta = r(1 +sin theta)

Sorry its hard to understand when written out, but if you have the book the diagrams there. Any help would be muchly appreciated.
Thanks


I did this question before i gave my C2.
Check out the answer and work backwords
Reply 5
Thats what I was thinking, thanks for trying though. Will get my techaer to explain it tomorrow. Cheeers
Reply 6
captnibby1234
I did this question before i gave my C2.
Check out the answer and work backwords

Got the answer but don't understand where the 1 comes from as there are no numbers given
Reply 7
clue: OEC is a right angled triangle r(1+sin theta)= r + r sin theta
Reply 8
thanks, where did you get the 1 from though?
Reply 9
This might be REALLY late, but here goes xD
We know that the radius of the sector = R. Therefore, the line OT = R (because the line OT is a radius, yep, captain obvious). Now, if we observe the line OT, you'll notice that a fraction of the line is the diameter of the circle (Note that the diameter of a circle is twice of the radius). If we take away the length of the radius of the circle inside the sector (from the line OT) starting from the point T you'll get the length of OC. From that, we can conclude that the line OC= R-r.
This is where you have to apply
Original post by Ummmidk
This might be REALLY late, but here goes xD
We know that the radius of the sector = R. Therefore, the line OT = R (because the line OT is a radius, yep, captain obvious). Now, if we observe the line OT, you'll notice that a fraction of the line is the diameter of the circle (Note that the diameter of a circle is twice of the radius). If we take away the length of the radius of the circle inside the sector (from the line OT) starting from the point T you'll get the length of OC. From that, we can conclude that the line OC= R-r.
This is where you have to apply


The question was posted in 2009 so yup really late.
In general people are discouraged from digging up old, long dead discussions.


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Reply 11
Original post by Ummmidk
This might be REALLY late, but here goes xD
We know that the radius of the sector = R. Therefore, the line OT = R (because the line OT is a radius, yep, captain obvious). Now, if we observe the line OT, you'll notice that a fraction of the line is the diameter of the circle (Note that the diameter of a circle is twice of the radius). If we take away the length of the radius of the circle inside the sector (from the line OT) starting from the point T you'll get the length of OC. From that, we can conclude that the line OC= R-r.
This is where you have to apply

thx