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# Need help with this DIFFICULT QUESTION :/

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1. is this A Level
2. Polar integration will help. But I'm assuming this is AS?
Actually looking at it polar would be of no use really.
3. Notice that it says OB and OC are arcs of circles.
4. AOB = Equilateral Triangle.

The angle = pie/3 as a result.

Find the area of the semi circle to the left.

Use pie/3 as an angle to find both sectors.

Add these up, then take away from the area of the whole circle.
AOB = Equilateral Triangle.

The angle = pie/3 as a result.

Find the area of the semi circle to the left.

Use pie/3 as an angle to find both sectors.

Add these up, then take away from the area of the whole circle.
But how do you know AOB is Equilateral Triangle?
6. Solomon paper L
7. I was thinking the same until i realised that:

AO = OB

AB = AO

therefore AO = AB = OB
But how do you know AOB is Equilateral Triangle?
You are told that arc OB is an arc of a circle with radius r and centre A.

So AO and AB must be equal since they have to be radii of that circle with centre A.

And AO = OB since they're both radii of the main circle.

So AO = AB = OB.
9. Same question was posted 3 days ago:
http://www.thestudentroom.co.uk/show...729&highlight=

should be useful^
10. (Original post by B_9710)
Polar integration will help. But I'm assuming this is AS?
Actually looking at it polar would be of no use really.
I mean, you could...

Spoiler:
Show
Observe that the circle formed by extending the arc OB has equation in polar coordinates . Given that the equation of the main circle is , it is easily seen that the first intersection of the two circles occurs at (in polars). Hence the area of the segment defined by sector AOB is given by:

Noting also that the area of sector OBC is and that the segment defined by sector OCD is equal in area to the one found above by symmetry, we see the shaded region is given by:

But this is slightly more involved than simply working out the segment directly (since, in this case, the arc is all circular and nice) and therefore excessive.
11. (Original post by notnek)
You are told that arc OB is an arc of a circle with radius r and centre A.

So AO and AB must be equal since they have to be radii of that circle with centre A.

And AO = OB since they're both radii of the main circle.

So AO = AB = OB.
I was thinking the same until i realised that:

AO = OB

AB = AO

therefore AO = AB = OB
AOB = Equilateral Triangle.

The angle = pie/3 as a result.

Find the area of the semi circle to the left.

Use pie/3 as an angle to find both sectors.

Add these up, then take away from the area of the whole circle.
(Original post by B_9710)
Notice that it says OB and OC are arcs of circles.
(Original post by SM45367)
Same question was posted 3 days ago:
http://www.thestudentroom.co.uk/show...729&highlight=

should be useful^
Thank you so much!!!

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