Solving with GeoGebra Discovery an Austrian Mathematics Olympiad problem: Lessons Learned

We address, through the automated reasoning tools in GeoGebra Discovery, a problem from a regional phase of the Austrian Mathematics Olympiad 2023. Trying to solve this problem gives rise to four different kind of feedback: the almost instantaneous, automated solution of the proposed problem; the measure of its complexity, according to some recent proposals; the automated discovery of a generalization of the given assertion, showing that the same statement is true over more general polygons than those mentioned in the problem; and the difficulties associated to the analysis of the surprising and involved high number of degenerate cases that appear when using the LocusEquation command in this problem. In our communication we will describe and reflect on these diverse issues, enhancing its exemplar role for showing some of the advantages, problems, and current fields of development of GeoGebra Discovery.
Comment: In Proceedings ADG 2023, arXiv:2401.10725