The nine-point conic: a rediscovery and proof by computer

Abstract

A heuristic description is given of the rediscovery with Sketchpad of a less-well-known, but beautiful, generalization of the nine-point circle to a nine-point conic, as well as an associated generalization of the Euler line. The author's initial analytic geometry proofs, which made use of the symbolic algebra facility of the TI-92 calculator, are also presented.