# 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 years, 3 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} $\boxed{123}$

Sort by:

Actual Yes

- 4 years, 3 months ago

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

- 4 years, 3 months ago

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

- 4 years, 3 months ago

How a triangle can have curved sides

- 4 years, 2 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).

- 4 years, 2 months ago

Actually yes you are right. I misunderstood the question

- 4 years, 2 months ago

how i can,understand noah

- 4 years, 2 months 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.

- 4 years ago

×