An intuitive geometry problem,
The ticket for the Chess world cup final is in the shape of a regular hexagon, with a side of 6 units. A circular stamp, of radius 2 units, is meant to be used to stamp the ticket in the center.
By, mistake the stamp get misaligned and stamps the ticket in such a way that the edge of the stamp exactly touches the vertex of the hexagon, while the center of the stamp lies on the line joining that vertex to the opposite vertex.
Find the portion of the stamp which falls outside the ticket.

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OpenStudy (anonymous):

diagram?

OpenStudy (anonymous):

That would spoil the problem to some extent ;)

OpenStudy (anonymous):

would there be 2 circles, one inside and one outside?

OpenStudy (anonymous):

There is only one stamp.

OpenStudy (anonymous):

well if the edge is outside then the circle must be inscribed inside

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OpenStudy (anonymous):

|dw:1338096917684:dw|

OpenStudy (anonymous):

cant really draw to scale

OpenStudy (anonymous):

is that how it should be?

OpenStudy (anonymous):

No.

OpenStudy (anonymous):

@experimentX got it right in the first time itself.

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OpenStudy (anonymous):

i'm confused

OpenStudy (anonymous):

me too :|

OpenStudy (binary3i):

is that \[(\pi -3\sqrt{3})/6\]

OpenStudy (anonymous):

No.

OpenStudy (anonymous):

|dw:1338097283187:dw|
Not perfect, but I believe the picture should look something like this.

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OpenStudy (anonymous):

Yes.

OpenStudy (anonymous):

And the area we are trying to find is:
|dw:1338097419327:dw|