Comparison of the Area of the Triangle Formed from the Symmedian Line and the Median Line

**MLA Style: **Yuni Silfiani, Mashadi, Sri Gemawati. "Comparison of the Area of the Triangle Formed from the Symmedian Line and the Median Line" International Journal of Mathematics Trends and Technology 67.2 (2021):68-73.

**APA Style: **Yuni Silfiani, Mashadi, Sri Gemawati(2021). Comparison of the Area of the Triangle Formed from the Symmedian Line and the Median Line. International Journal of Mathematics Trends and Technology, 68-73.

**Abstract**

This paper discusses the area of a triangle formed from the symmedian line and the median line. This discussion includes determining the length of the symmedian line and the comparison of the area of a triangle formed from the symmedian line and the median line. The proof is done by using a very simple method, which is by comparing the bases of the triangles formed and using several theorems such as Stewart's theorem and Steiner’s theorem.

**Reference**

[1] G. W. I. S. Amarasinghe, On the Standard Lengths of Angle Bisectors and the Angle Bisector Theorem, Global Journal of Advanced Research on Classical and Modern Geometries, (2012) 15-27.

[2] Amelia, Mashadi and S. Gemawati, Alternative Proofs for the Lenght of Angle Bisectors Theorem on Triangle, International Journal of Mathematics Trens and Technology, 66(2020) 163-166.

[3] D. Dekov, Computer-Generated Mathematics:The Symmedian Point, Mathematika Pannonica, 10 (2008) 1-36.

[4] D. Grinberg, Ehrmanns Third Lemoine Circle, Journal of Classical Geometry, 1(2012) 40-52

[5] C. Kimberling, Trilinear Distances Inequalities for the Symmedian Point, Centroid, and Other Triangle Center, Forum Geometricorum, 10 (2010), 135-139.

[6] S.N Kiss and P. Yiu, On the Tucker Circles, Forum Geometricorum, 17(2017) 157-175.

[7] B. Kolar, Symmedians and the Symmedian Center of the Triangel in an Isotropic Plane, Mathematika Pannonica, 17(2)(2006) 287-301.

[8] S. Luo and C. Pohoata, Let’s Talk About Symmedians!, NC School of Science and Mathematics, Princeton University, USA, (1993).

[9] J. S. Mackay, Early History of the Symmedian Point, Proceedings of the Edinburgh Mathematical Society 11(1892-93) 92-103.

[10] J. S. Mackay, Symmedians of a Triangle and Their Concomitant Circles, Proceedings of the Edinburgh Mathematical Society 14 (1895) 37-103.

[11] Mashadi, Geometry (in Indonesian: Geometri), Second Edition, UR Press, Pekanbaru, (2015).

[12] Mashadi, Advanced Geometry (in Indonesian: Geometri Lanjut), UR Press, Pekanbaru, (2015).

[13] J. Sadek, M.B Yaghoub and N.H Rhee, Isogonal Conjugates in a Tetrahedron, Forum Geometricorum, 16(2016) 43-50.

[14] D. Trisna, Mashadi and S.Gemawati, Angle Trisector in the Three Angles, IOSR Journal of Mathematical 16 (2020) 11-18.

[15] A. Wardiyah, Mashadi and S. Gemawati, Relationship of Lemoine Circle with a Symmedian Point, Journal of Mathematical Sciences, 17(2016) 23-33.

[16] Y. Zhao. Three Lemmas in Geometry, Canada IMO Training Handout, Winter Camp, (2010).

**Keywords : **Area comparison of triangle, median, symmedian, symmedian line length.