Three different circles are drawn in the same plane. What is the greatest number of points at which at least two of these circles can intersect?

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Three different circles are drawn in the same plane. What is the greatest number of points at which at least two of these circles can intersect?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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hm, I'm not sure if there's an intuitive way to solve this, but... |dw:1437018135749:dw|
|dw:1437018182895:dw|
gives me 6 points of intersection

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Oh okay so basically you have to draw it out to solve?
well, that's how I would try it. the highest number I can get is 6, unless someone can prove me wrong? haha @ganeshie8
That's okay! It makes sense to me now, thank you so much!! :)
I'd do the same. 6 is what im getting too..
Alright! Thank you!

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