Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON TRIANGLES ASSOCIATED WITH A CURVE

  • Kim, Dong-Soo (Department of Mathematics Chonnam National University) ;
  • Kim, Dong Seo (Department of Mathematics Chonnam National University) ;
  • Kim, Young Ho (Department of Mathematics Kyungpook National University)
  • Received : 2014.04.23
  • Published : 2015.05.31
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Abstract

It is well-known that the area of parabolic region between a parabola and any chord $P_1P_2$ on the parabola is four thirds of the area of triangle ${\Delta}P_1P_2P$. Here we denote by P the point on the parabola where the tangent is parallel to the chord $P_1P_2$. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles ${\Delta}P_1P_2PQ$ where Q is the intersection point of two tangents to X at $P_1$ and $P_2$ we establish some characterization theorems for parabolas.

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References

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