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# C2 circles question watch

1. 2 circles have radius of 4cm.
The center of each circle lies on the circumference of the other.
Find the exact area which is common to both circles.
Thank you
2. I'd start by drawing a line between the two points of intersection. Can you then see the area of one of the bits?
3. so i now have a semi-circle right
4. I wish I could draw!!

If the two circles are the same size, and the centre of one is on the edge of the other, they intersect twice. The two points of intersection are each about a third of the circumference apart
5. (Original post by ian.slater)
I wish I could draw!!

If the two circles are the same size, and the centre of one is on the edge of the other, they intersect twice. The two points of intersection are each about a third of the circumference apart
Out of interest, how do you know this?

And I would have thought they are the same size since they both have the same radius of 4cm.
6. Now join the two points of intersection, with a line that is a chord is each circle. In C2 you have probably learned how to work out the area of one bit, which is the difference between a sector (like a large slice of a round cake) and a triangle.

So you need to find out the angle subtended at the centre of a circle by the chord you have drawn.

When you mark in the lengths you know, you (and Matthew) will see where the third comes from
7. can you give me the sum i need to i think i might understand it better that way as, im not fully understanding you at the moment
sorry

8. 2 (equal) segments..
9. Look just at one circle. Draw lines (radii) from the centre to the two points of intersection. Draw another line to the centre of the second circle.

All the radius lines are 4cm long
10. I tried to do this using integration and it ended up ridiculousy complicated

If anyone else can do the integration, the equations of the two circles can be:

and
11. (Original post by CrazyChris)

2 (equal) segments..
Yay
12. (Original post by ian.slater)
Now join the two points of intersection, with a line that is a chord is each circle. In C2 you have probably learned how to work out the area of one bit, which is the difference between a sector (like a large slice of a round cake) and a triangle.

So you need to find out the angle subtended at the centre of a circle by the chord you have drawn.

When you mark in the lengths you know, you (and Matthew) will see where the third comes from
What does subtended mean?
13. (Original post by mathew551)
What does subtended mean?
If the chord is AB, and the centre is O then the angle AOB is said to be the angle subtended by AB at O. Really.
14. Use Pythagoras' theorum to work out half the distance of the line that can be drawn that connects the two points of intersection (the chord)? You can then work out the area of one triangle using Area = base x height divided by 2?

15. Area (segment) = Area (sector) - Area (triangle)

Now, i've gotta go, so enjoy
16. according to my friend who asked the teacher the answer is
16(2pi/3 - sqr3/2)
how did the teacher get that
17. (Original post by CrazyChris)

Area (segment) = Area (sector) - Area (triangle)

Now, i've gotta go, so enjoy
Thank you i get it now
Thank you to everyone else who tried to help

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