The discussion revolves around finding the side length of an equilateral triangle given the distances from an inner point to the vertices. The problem involves geometric reasoning and potentially the application of trigonometric principles.
The discussion does not reach a consensus, as multiple approaches are suggested, and no definitive solution is presented.
Some assumptions regarding the properties of equilateral triangles and the implications of the geometric transformations are not fully explored or stated.
Rotate the trianlge by 60 degrees about the point C. Let $P'$ be the new position of $P$. Then $\angle P'PA=90$. Thus we get a triangle $CPA$ with $\angle CPA=150$ and $PC=3, PA=4$. To find $AC$.Albert said:
Brilliant solution!Albert said:
