Skinny Triangle

Geometry Level 5

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

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