Two circles have the same radius 1 unit. If each circle passes through the centre of the other circle, what is the area common to the two circles?

Area of two circles is 2pi. But how could I find the common area?

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- October 31st 2010, 05:03 AMgetonCommon area of circles
Two circles have the same radius 1 unit. If each circle passes through the centre of the other circle, what is the area common to the two circles?

Area of two circles is 2pi. But how could I find the common area? - October 31st 2010, 05:12 AMUnknown008
You'll need to make a sketch.

You'll see that the common area can be divided into 6 parts of which there are 2 equilateral triangles and 4 equal segments.

Can you try out to find the area now? - October 31st 2010, 06:04 AMgeton
Attachment 19540

So area of two equilateral triangles is

Area of 4 segment =

Therefore, enclosed area =

Is this right? - October 31st 2010, 07:07 AMearboth
- October 31st 2010, 07:22 AMUnknown008
Yup, well done (Smile)