Solving a problem with GeoGebra current possibilities and limits of CAS tools

Abstract In the article we show what a Dynamic Geometry Environment ( DGE ) and Computer Algebra System ( CAS ) software is capable of exploring, computing and proving a geometry problem that is closely related to the well-known Wallace-Simson theorem. In our case, this problem turns out to be quite difficult for some software tools incorporated in the DGE software. The computation of a searched locus by the software works well in our case, but the problem must be formulated in a specific way. In addition to the conclusions attained by DGE software, we present computer-aided analytical solutions in the second half of paper. It is shown that the use of non-degeneracy conditions before elimination leads to a significant reduction of the computation time.