  The non-uniqueness of a rational parametrization of a rational plane curve
may influence the process of computing envelopes of 1-parameter families of
plane curves. We study envelopes of family of circles centred on a regular
trifolium and its offsets, paying attention to different parametrizations. We
use implicitization both to show that two rational parametrizations of a curve
are equivalent, and to determine an implicit equation for the envelope under
study. The derivation of an implicit equation of an offset follows another
path, leading to new developments of the package GeoGebra Discovery. As an
immediate symbolic result, we obtain that in the general case the offset curve
of a regular trifolium is an algebraic curve of degree 14. We illustrate this
fact by providing a GeoGebra applet that computes such curves automatically and
visualizes them in a web browser.
