Solutions: https://swerc.eu/theme/slides/problemanalysis.pdf

I have a problem in Problem-K. The solution states that we find the distance of the point furthest away from each side of the convex hull individually. But I can’t see how to do that in O(n) time. It is trivial to do it in O(n^2) but I don’t know to find it in amortized O(n) time. Can someone help me?