Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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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)
  • Received : 2016.12.30
  • Accepted : 2017.01.16
  • Published : 2017.03.25
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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.

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References

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