Generalisation of an IMO geometry problem

According to Mitchelmore [1], generalisations are the cornerstone of school mathematics, covering various aspects like numerical generalisation in algebra, spatial generalisation in geometry and measurement, as well as logical generalisations in diverse contexts. The process of generalising lies at the heart of mathematical activity, serving as the fundamental method for constructing new knowledge [2, 3]. In this paper we will generalise an interesting geometry problem that appeared in the 1995 edition of the International Mathematical Olympiad (IMO) [4].