I'm curious... Is it true, and, if so, is it straightforward to show that the maximum area triangle that can squeeze between these circles is equilateral?

You can model this on a co-ordinate grid, circles of radius 1 centered at (0,-1) and (+-1, \(\sqrt{3}-1\)). I couldn't really get anywhere, though. Probably a geometric solution is optimal, but I've never been good at those.

It can't have curved sides... I am talking about squeezing a triangle (which has straight sides) in that little space in the middle (which has curved sides).

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TopNewestYou can model this on a co-ordinate grid, circles of radius 1 centered at (0,-1) and (+-1, \(\sqrt{3}-1\)). I couldn't really get anywhere, though. Probably a geometric solution is optimal, but I've never been good at those.

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how i can,understand noah

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Actually yes you are right. I misunderstood the question

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How a triangle can have curved sides

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It can't have curved sides... I am talking about squeezing a triangle (which has straight sides) in that little space in the middle (which has curved sides).

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Actual Yes

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Sounds good... Do you know how to show it?

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Yes The area of all 4 circles are equal to the area of the 4 triangles

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