# 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
1 year, 5 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.

- 1 year, 2 months ago

how i can,understand noah

- 1 year, 4 months ago

Actually yes you are right. I misunderstood the question

- 1 year, 4 months ago

How a triangle can have curved sides

- 1 year, 4 months ago

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).

- 1 year, 4 months ago

Actual Yes

- 1 year, 5 months ago

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

- 1 year, 5 months ago

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

- 1 year, 5 months ago