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Maximizing a triangle

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?

Note by Geoff Pilling
7 months, 2 weeks ago

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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.

Alex Li - 4 months, 2 weeks ago

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how i can,understand noah

Biswajit Barik - 5 months, 4 weeks ago

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Actually yes you are right. I misunderstood the question

Shrunkhal Wankhede - 6 months ago

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How a triangle can have curved sides

Shrunkhal Wankhede - 6 months ago

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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).

Geoff Pilling - 6 months ago

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Actual Yes

Noah Smalls - 7 months, 1 week ago

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

Geoff Pilling - 7 months, 1 week ago

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

Noah Smalls - 7 months, 1 week ago

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