Homothetic transformations and geometric loci: properties of triangles and quadrilaterals

In this paper, we use geometric transformations to find some interest- ing properties related with geometric loci. In particular, given a trian- gle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadri- laterals) when one vertex moves on the circumcircle of the figure are considered. These loci are studied in paragraphs 3 and 4. By means of the homothetic transformations some properties of triangles and quadrilaterals are found. The study of these properties can be used, with profit, in a classroom activity supported by Dynamic Geometry System.