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# P1 maths watch

1. ok can you help me with this question:
"in the diagram the chord AB of the circle with centre O is such that AOB = 1.4 radians. given that the shaded area is 4cm^2 find the radius of the circle correct to 2 decimal places."

would this be the right idea? 1/2r^2•-1/2bcsin•=4

• is theta (the angle)

i have attached a picture of it below
Attached Images

2. (Original post by greenie787)
ok can you help me with this question:
"in the diagram the chord AB of the circkw with centre O is such that AOB = 1.4 radians. given that the shaded area is 4cm^2 find the radius of the circle correct to 2 decimal places."

would this be the right idea? 1/2r^2•-1/2bcsin•=4

• is theta (the angle)

i have attached a picture of it below
Use
area of the sector = r^2 x angle
and

area of the triagle = r^2 x sin angle

to form simulatius equation (they minus 2 make that shaded area) the r is the only variable!!!!

is that any help???
3. (Original post by Harveer)
Use
area of the sector = r^2 x angle
and

area of the triagle = r^2 x sin angle

to form simulatius equation (they minus 2 make that shaded area) the r is the only variable!!!!

is that any help???
i thought it was 1/2 bc sin angle to find the area of the triangle?
4. That diagram cheered me up a bit
5. I get the shaded area to be:

As = 0.5*q*R^2 - R(sin(q/2)*cos(q/2))

where q is theta
6. (Original post by greenie787)
i thought it was 1/2 bc sin angle to find the area of the triangle?
well, boh of them r used...but it fairly depends !!!
7. Area of the sector is

1/2.r^2.[theta]

Area of the triangle is

1/2.r^2.sin[theta]

The shaded segment is their difference:

1/2.r^2.([theta] - sin[theta])

These formulae only work when theta is in radians, btw.

You know this area is 4cm^2, and theta is 1.4, so it all becomes

4 = 1/2.r^2.(1.4 - sin(1.4))

which you can solve for r. My arithmetic is wretched but I got 4.39cm (2dp)

Hope this helps.

Jon
8. thanks every 1 i should be able to work it out now.

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