Locus problems concerning centroids of a cyclic quadrilateral and two classic cubic curves

On his website dedicated to questions and investigations arising out of dynamic geometry technology, Michael de Villiers has a series called Geometry Loci Doodling [1]. These are locus problems connected to the centroids of cyclic quadrilaterals – ‘centroids’ in the plural, for there are three diffe...

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Bibliographic Details
Published in:Mathematical gazette 2022-07, Vol.106 (566), p.247-257
Main Author: Fried, Michael N.
Format: Article
Language:English
Subjects:
Apexes
Centroids
Loci
Quadrilaterals
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Summary:On his website dedicated to questions and investigations arising out of dynamic geometry technology, Michael de Villiers has a series called Geometry Loci Doodling [1]. These are locus problems connected to the centroids of cyclic quadrilaterals – ‘centroids’ in the plural, for there are three different kinds of centroid depending whether one understands the quadrilateral in terms of its vertices, perimeter or area. The corresponding centroids are the point-mass centroid, the perimeter-centroid, and the lamina-centroid. In each case, de Villiers keeps three vertices of the quadrilateral fixed on the circumcircle, and then traces the locus of the different centroids as the fourth point moves round the circle. In this paper, I shall take a brief look at the point-mass centroid and then a lingering view of the lamina-centroid.
ISSN:0025-5572
2056-6328
DOI:10.1017/mag.2022.65