Let \(ABC\) be a triangle such that \(AB=24\) is the diameter of of a circle \(O\). Points \(F\) and \(E\) lie on the intersection of the circle and lines \(BC\) and \(AC\), respectively, such that \(BF=1\) and \(AE=3\). Find the perimeter of triangle \(ABC\). Round your answer to the nearest integer.
This problem was created while accidentally misinterpreting an OMO problem. :D