Three coloured equilateral triangles share three vertices. Prove that the triangle formed by their centres is also equilateral.^{1}This puzzle is also known as Napoleon’s Theorem.

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## Solution

## Poem

We are the 4 triangles quartet

As you can see

We have a lot of angles

Without being caught in a tangle

We live together carefully

We believe in rimes and poetry

We know what the poet meant to say

And find the words along the way

We are the 4 so pretty

You will love our harmony

## 2 replies on “Triangle quartet II”

https://en.wikipedia.org/wiki/Napoleon%27s_theorem

A related problem is “Napoleon Strikes Again”, August 31, 2022.