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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
4 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 · 1 month, 2 weeks ago

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how i can,understand noah Biswajit Barik · 2 months, 3 weeks ago

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Actually yes you are right. I misunderstood the question Shrunkhal Wankhede · 2 months, 4 weeks ago

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How a triangle can have curved sides Shrunkhal Wankhede · 2 months, 4 weeks ago

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@Shrunkhal Wankhede 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 · 2 months, 4 weeks ago

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Actual Yes Noah Smalls · 4 months, 1 week ago

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@Noah Smalls Sounds good... Do you know how to show it? Geoff Pilling · 4 months, 1 week ago

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@Geoff Pilling Yes The area of all 4 circles are equal to the area of the 4 triangles Noah Smalls · 4 months, 1 week ago

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