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?

#Geometry

Easy Math Editor

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Comments

Actual Yes

Noah Smalls - 4 years, 2 months ago

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

Geoff Pilling - 4 years, 2 months ago

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

Noah Smalls - 4 years, 2 months ago

How a triangle can have curved sides

shrunkhal wankhede - 4 years 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).

Geoff Pilling - 4 years ago

Actually yes you are right. I misunderstood the question

shrunkhal wankhede - 4 years ago

how i can,understand noah

Biswajit Barik - 4 years ago

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 - 3 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$