• Journal for History of Mathematics
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• v.17 no.2
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• pp.61-72
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• 2004

In this article we study on didactic transposition and enlargement of the Ceva theorem(if three cevians AX, BY, CZ, one through each vertex of a triangle ABC, are concurrent, then $\frac{BX}{XC}\frac{CY}{YA}\frac{AZ}{ZB}$ = 1). We suggest inverse of the Ceva theorem, some different forms of the Ceva theorem(oriented segment form, trigonometric form, vector form), enlarged the Ceva theorem of polygon and tetrahedron, and in detail propose these proofs.

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.621-634
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• 2006

In this study we describe the characteristics of solving geometry problems related with the ratio of segments using the principle of the lever and the center of gravity, compare and analyze this problem solving method with the traditional Euclidean proof method and the analytic method.

• Journal of Integrative Natural Science
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• v.10 no.1
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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.