# 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
2 years, 9 months ago

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## Comments

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Actual Yes

- 2 years, 9 months ago

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

- 2 years, 9 months ago

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

- 2 years, 9 months ago

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How a triangle can have curved sides

- 2 years, 8 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).

- 2 years, 7 months ago

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Actually yes you are right. I misunderstood the question

- 2 years, 7 months ago

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how i can,understand noah

- 2 years, 7 months 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.

- 2 years, 6 months ago

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