• Honam Mathematical Journal
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• v.39 no.2
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• pp.247-258
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• 2017

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.