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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.