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http://dx.doi.org/10.5831/HMJ.2017.39.2.247

VARIOUS CENTROIDS OF QUADRILATERALS  

Lee, Seul (Department of Mathematics, Chonnam National University)
Kim, Dong-Soo (Department of Mathematics, Chonnam National University)
Park, Hyeon (Department of Mathematics, Chonnam National University)
Publication Information
Honam Mathematical Journal / v.39, no.2, 2017 , pp. 247-258 More about this Journal
Abstract
For a quadrilateral 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. It is well known that P satisfies $G_0=G_1$ or $G_0=G_2$ if and only if it is a parallelogram. In this note, we investigate various quadrilaterals satisfying $G_1=G_2$. As a result, for example, we show that among circumscribed quadrilaterals kites are the only ones satisfying $G_1=G_2$. Furthermore, such kites are completely classified.
Keywords
Centroid; perimeter centroid; rhombus; parallelogram; circumscribed quadrilateral;
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Times Cited By KSCI : 5  (Citation Analysis)
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