A generalisation of the nine-point circle and Euler line

Abstract

To most people, including some mathematics teachers, geometry is synonymous with ancient Greek geometry, especially as epitomised in Euclid's Elements of 300 BC. Sadly, many are not even aware of the significant extensions and investigations of Apollonius, Ptolemy, Pappus, and many others until about 320 AD. Even more people are completely unaware of the major developments that took place in synthetic Euclidean plane geometry from about 1750-1940, and more recently again from about 1990 onwards (stimulated in no small way by the current availability of dynamic geometry software).