  Euler's inequality $R\geq 2r$ can be investigated in a novel way by using
implicit loci in GeoGebra. Some unavoidable side effects of the implicit locus
computation introduce unexpected algebraic curves. By using a mixture of
symbolic and numerical methods a possible approach is sketched up to
investigate the situation. By exploiting fast GPU computations, a web
application written in CindyJS helps in understanding the situation even
better.
