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square inscribed in triangle

This was frustrating. Much thanks to Charlie for his procedural step-by-step construction directions, but alas I still couldn't get this one. It seemed that no matter what I tried to do, I eventually got to the point where I had gotten to the last puzzle piece only to find that that point I was looking to connect was an intersection and not a point. As far as I can tell, it seems as though an intersection can only occur between two objects? Or is it that I am not seeing the underlying relationship that would make such an intersection impossible?