In the discussion, the problem involves finding the maximum distance \( PC \) in an equilateral triangle \( \triangle ABC \) where the lengths \( AB = BC = CA \) are equal. Given the distances \( PA = 2 \) and \( PB = 3 \), participants explore geometric properties and potential configurations of point \( P \) relative to the triangle. The solution requires applying principles of triangle geometry and optimization techniques to determine the maximum value of \( PC \). The discussion highlights the importance of understanding the triangle's symmetry and the relationships between the points. Ultimately, the goal is to derive the maximum distance \( PC \) based on the given constraints.
