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AL Maths Question-need some help!

The diagram shows the sector OAB of a circle with centre O, radius 12cm and angle 1.2 radians. The line AC is a tangent to the circle with centre O, and OBC is a straight line. The region R is bounded by the arc AB and the lines AC and CB. The line BD is parallel to AC. Find the perimeter of DAB.

(Will try to add a pic of the diagram) q16.png - OneDrive
This question is from Edexcel year 2 Maths chapter 5 exercise 5D
(edited 2 months ago)
Reply 1
Original post by pigeonwarrior
The diagram shows the sector OAB of a circle with centre O, radius 12cm and angle 1.2 radians. The line AC is a tangent to the circle with centre O, and OBC is a straight line. The region R is bounded by the arc AB and the lines AC and CB. The line BD is parallel to AC. Find the perimeter of DAB.

(Will try to add a pic of the diagram) q16.png - OneDrive
This question is from Edexcel year 2 Maths chapter 5 exercise 5D

Should be some straightorward trig? Cant see your images, but just try and describe what you did/what the problem is.
Original post by mqb2766
Should be some straightorward trig? Cant see your images, but just try and describe what you did/what the problem is.

I don't know how to figure out line DA and line BD. Arc AB is easy as it is just 12 x 1.2 which is 14.4. The perimeter of DAB would be arc AB+line BD+line DA and I'm confused about the last two. I looked at the solution bank and yes they are using basic SOH CAH TOA to figure out the lengths of BD and DA but how can they assume that OD is the same as OA (OA is the base of the triangle and that is 12cm). D cuts OA at one point so OD is obviously smaller than OA. But they are assuming that OD is 12cm like OA and that is where I am confused.
Reply 3
Original post by pigeonwarrior
I don't know how to figure out line DA and line BD. Arc AB is easy as it is just 12 x 1.2 which is 14.4. The perimeter of DAB would be arc AB+line BD+line DA and I'm confused about the last two. I looked at the solution bank and yes they are using basic SOH CAH TOA to figure out the lengths of BD and DA but how can they assume that OD is the same as OA (OA is the base of the triangle and that is 12cm). D cuts OA at one point so OD is obviously smaller than OA. But they are assuming that OD is 12cm like OA and that is where I am confused.

You have the right triangle ODB which has hypotenuse 12 and angle 1.2 rad. So you can get OD and BD, and the former gives AD by subtracting it from the radius OA
Original post by mqb2766
You have the right triangle ODB which has hypotenuse 12 and angle 1.2 rad. So you can get OD and BD, and the former gives AD by subtracting it from the radius OA

How do you know that the hypotenuse is 12?
Reply 5
Original post by pigeonwarrior
How do you know that the hypotenuse is 12?

OB is a radius = 12
Original post by mqb2766
OB is a radius = 12

https://qr.ae/pKwQEu

Here is the question with the diagram. Also, would it be that OC is 12 rather than OB? I'm a bit stuck on this one!

edit: I also included the solutions which are not really making sense to me
(edited 2 months ago)
Reply 7
Original post by pigeonwarrior
https://qr.ae/pKwQEu

Here is the question with the diagram. Also, would it be that OC is 12 rather than OB? I'm a bit stuck on this one!

edit: I also included the solutions which are not really making sense to me

OA is a radius just like OB, after all AB is an arc of the circle. A bit like the other question, youre overthinking it. OBD is a right triange where the hypotenuse OB is a radius = 12. Then its simple trig to get the other two sides ...
(edited 2 months ago)
Original post by mqb2766
OA is a radius just like OB, after all AB is an arc of the circle. A bit like the other question, youre overthinking it. OBD is a right triange where the hypotenuse OB is a radius = 12. Then its simple trig to get the other two sides ...

I see it now, thank you so much!!!

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