I'm working on a problem of inscribing equilateral triangle for some time now and it goes like this :
using only a foot rule and a compasses , show a way of inscribing an equilateral triangle into an arbitrary triangle.
I looked throughout the internet and didn't find any clues about the path to the solution of this problem. the direction I am thinking about is : the problem can be solved easily for inscribing an equilateral triangle into another equilateral triangle by choosing the middle of each side of the outer triangle to be the vertices of the inscribed triangle , I am trying to found the general rule for the case where the outer triangle is an arbitrary one based on the observation of the described above equilateral triangle. I can't seem to get the right general rule. after I will find a general way to do it I will think about how to accomplish it by using only a foot rule and a compasses.
I think that it can be useful for a range of such problems to get the right direction to the solution of this problem.
Thanks ,