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http://dx.doi.org/10.5831/HMJ.2017.39.1.127

PERIMETER CENTROIDS AND CIRCUMSCRIBED QUADRANGLES  

Ahn, Seung Ho (Department of Mathematics, Chonnam National University)
Jeong, Jeong Sook (Department of Mathematics, Chonnam National University)
Kim, Dong-Soo (Department of Mathematics, Chonnam National University)
Publication Information
Honam Mathematical Journal / v.39, no.1, 2017 , pp. 127-136 More about this Journal
Abstract
For a quadrangle P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. If $G_0$ is equal to $G_1$ or $G_2$, then the quadrangle P is a parallelogram. We denote by M the intersection point of two diagonals of P. In this note, first of all, we show that if M is equal to $G_0$ or $G_2$, then the quadrangle P is a parallelogram. Next, we investigate various quadrangles whose perimeter centroid coincides with the intersection point M of diagonals. As a result, for an example, we show that among circumscribed quadrangles rhombi are the only ones whose perimeter centroid coincides with the intersection point M of diagonals.
Keywords
Centroid; perimeter centroid; rhombus; parallelogram; circumscribed quadrangle;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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