A DYNAMIC VIEW OF SOME GEOMETRIC LOCI VIA GEOGEBRA

Abstract

We present in this work dynamic experiences that explore interesting geometric loci,
such as Miquel points, Fermat points, Nagel points, and Gergonne points. In these
dynamic approaches, accessible through external links to pages on the GeoGebra platform,
readers can change parameters through sliders and observe, as the parameters
vary, whether the introduced changes satisfy the hypotheses that define the geometric
loci. Additionally, we utilize GeoGebra to create two-dimensional geometric figures.
In addition to providing definitions, we offer proofs of the theorems that establish the
uniqueness of the covered geometric loci. Some of the proofs introduced in this work
involve the concept of isotomic cevians, which needs more coverage in the existing literature.
In summary, GeoGebra is an invaluable tool for constructing dynamic approaches
to explore geometric loci. It empowers students to test hypotheses both before and
after formal demonstrations. One concludes that GeoGebra is a versatile software that
can be effectively integrated into geometry education at all levels.

Keywords: Isotomic cevians, Miquel’s point, Fermat’s points, Gergonne’s point, Nagel’s
point.