• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.25-34
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• 2015

In this paper we characterize the isogonal and isotomic conjugates of conic. Every conic can be expressed by a quadratic rational B$\acute{e}$zier curve having control polygon $b_0b_1b_2$ with weight w > 0. We show that the isotomic conjugate of parabola and hyperbola with respect to ${\Delta}b_0b_1b_2$ is ellipse, and that the isotomic conjugate of ellipse with the weight $w={\frac{1}{2}}$ is identical. We also find all cases of the isogonal conjugate of conic with respect to ${\Delta}b_0b_1b_2$. Our characterizations are derived easily due to the expression of conic by the quadratic rational B$\acute{e}$ezier curve in standard form.

• 통합자연과학논문집
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• 제10권1호
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• pp.27-32
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• 2017

In this paper we consider the two tangent lines of isogonal and isotomic conjugates of the line at both vertices of a given triangle. We find the necessary and sufficient condition for the two tangent lines of isogonal or isotomic conjugates of the line at both vertices and the median line to be concurrent. We also prove that every line whose isogonal conjugate tangent lines at both vertices are concurrent with the median line intersects at a unique point. Moreover, we show that the three intersection points correspond to the vertices of triangle are collinear.