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**M0**

It turns out, the solution is an equilateral triangle.

This might seem obvious, eg by using intuitive notions of symmetry. However, it is still interesting to consider **why** this is correct.

Here (left) we move point A slightly. What happens to the 'height' of the triangle?

This suggest that the given position of A is a maximum - - at least, a **local** one. But what happens if we move B and/or C ?

We explore this conjecture on the next page.