Günter Rote:

The largest inscribed triangle and the smallest circumscribed triangle of a convex polygon: an overview of linear-time algorithms

Abstract

This note gives a self-contained development of linear-time algorithms for largest inscribed and the smallest circumscribed triangle, starting from scratch. The essential ideas and inspirations have been taken from the literature, but I have tried to streamline the presentation for simplicity. The same underlying optimality condition appears in various guises in the literature. I hope that my presentation contributes to the clarification of the ideas underlying the algorithms.