...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 2 | Year 2021 | Article Id. IJMTT-V67I2P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I2P510

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


Yuni Silfiani, Mashadi, Sri Gemawati
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.

Keywords
Area comparison of triangle, median, symmedian, symmedian line length.
References

[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).

Citation :

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 (IJMTT), vol. 67, no. 2, pp. 68-73, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I2P510

  • PDF
  • Abstract
  • Keywords
  • References
  • Citation
Abstract Keywords References Citation
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2025 Seventh Sense Research Group® . All Rights Reserved