The construction: Take any triangle. Construct an equilateral triangle on the outside of each edge. Connect the free (outside) vertex of each equilateral triangle with the opposite vertex of the original triangle (A -> B in the figure - I've only drawn one of the equilateral triangles).
The investigation: What is true about the intersection(s) of these three lines? Can you find out anything about the point(s) where they intersect in relation to the original triangle? Construct the circumcircles of the equilateral triangles - notice anything interesting?
Did you find anything in here that you could pose as a challenge problem for us or for others?
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