If we draw a line through the point in the center that is parallel to
one side, then the problem is exactly the same as showing that the
2 perpendiculars in the top triangle sum up to the length of a
perpendicular for that top triangle. If we draw a line through the
point that is parallel to one of the original sides and consider only
the picture for the top triangle, then it is clear that the
perpendicular for the smallest triangle is a perpendicular from the vertex.
Since we are dealing with equilateral triangles, if we rotate this small
triangle, we see that the perpendicular added to the other perpendicular
in the top triangle will add to the perpendicular for the top triangle,
and then when we add the three together we get the result.
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