Symmedian Development of the Trimedian and Trisector

International Journal of Mathematics Trends and Technology (IJMTT)
© 2021 by IJMTT Journal
Volume-67 Issue-3
Year of Publication : 2021
Authors : Eka Jumianti, Mashadi, Sri Gemawati


MLA Style: Eka Jumianti, Mashadi, Sri Gemawati  "Symmedian Development of the Trimedian and Trisector" International Journal of Mathematics Trends and Technology 67.3 (2021):21-27. 

APA Style: Eka Jumianti, Mashadi, Sri Gemawati(2021). Symmedian Development of the Trimedian and Trisector International Journal of Mathematics Trends and Technology, 21-27.

In general, a lot of discussion on the line discusses the symmedian point. This paper discusses the reflection of trimedian and trisector. The discussion is about the side lengths of the symmedian and the area of the symmedian of triangle. The proof is done using a very simple method, namely by using the concept of the height line on the triangle and the trigonometric concepts of the triangle.


[1] Amarsinghe., G.W.I.S. The Convex Coordinates of The Symmedian Point, Global Journal of AdvancesResearch on Classical and Modern Geometries. (2002) 15-27.
[2] Arisa, Y. Mashadi and S. Gemawati., Modification of the Varignon Theorem on The Triangle, International Journal of Recent Scientific Research, 11(2020) 39642-39646.
[3] Begovic, Z.K, Super, R. K,Brkic, J. B, Volenec, V., Symmedian and Symmedian Center of The Triangle In an Isotropic Plane, Mathematica Panonica,10 17/2 (2006) 287-301.
[4] Boyd, J. N and Rachowdury, P.N., The Convex Coordinates of The Symmedian Point, Mathematics and Computer Educations, (2014) 51-56.
[5] Brian, S., A Simple Geometric Proof of Morley’s Trisector Theorem, Applied Probability Trust, (2009).
[6] Cesare, D., A Vector-based Proof of Morley’s trisector Theorem, Forum Geometricorum, 13(2013) 233-235.
[7] Darij, G., Ehrmann’s Third Lemoine Circle, Massachusetts Institute of Technology, 40-52.
[8] Dekov, D., Computer-generated Mathematics: The Symmedian Point, Mathematica Panonica, 10 (2008) 1-36.
[9] Dekov, D., Lemoine-Kiepert Point, Journal of Computergenerated Euclidean Geometry, 9(2008) 1-8.
[10] Grinberg, D., Ehrmanns Third Lemoine Circle.Journal of Classical Geometry, 1(2012) 40-52.
[11] Husna R, Mashadi dan S. Gemawati., Morley’s Theoremourter Trisektor on Triangels and Isosceles Trapezoid, International Journal of Current Advancesd Research, 18(2019) 18778-18780.
[12] Kiss, S. N, and Yiu, P., On The Tucker Circle, Forum Geometricorum,17 (2017) 157-175.
[13] Kuruklis, S. A., Trisector like Bisector with Equilaterals Instead of Point, Cubo A Mathematical Journal, 16(2)(2014) 71-110.
[14] Mashadi, Advanced Geometry (in Indonesian: Geometry Lanjut) , UR Press, Pekanbaru,(2015).
[15] Mashadi, Advanced Geometry II ( in Indonesian: Geometri Lanjut II), UR Press, Pekanbaru,(2020).
[16] Mirella, K. Z., Curves of Centoids, Gergonne Points and Symmedian Centers in Triangle Pencils in Isotropic Plane, Rad Hazu Matematicke Znanosti, 534 (2018) 119-127.
[17] Oliver.P. N., Pierre Varignon and the Parallelogram Theorem, Mathematic Teacher of Mathematic, 94(2001) 406-408.
[18] Palatnik, A., Proof Without Words Varignon’s Theorem, College Mathematic Journal, 48(2017) 354.
[19] Roland. C., Morley’s Trisector Theorem, Formalized Mathematics, 23(2015) 75-79.
[20] Sammy. L. and Cosmin P., Lets Talk About Symmedian, N.C School of Science and Mathematics,Princeton University,USA,(1993).
[21] Singhal, S., On the Orthogonality a Median and a Symmedian, Mathematica Panonica, 17(2017) 203-206.
[22] Trina, D., Mashadi and S. Gemawati, Angle Trisector in the Triangle, IOSR Journal of Mathematics, 16(2020)11-18.
[23] Walls, N., An Elementary Proof of Morley Trisector Theorem, Edinburgh Mathematical Note, 34(2008) 12-13.
[24] Wardiyah, A., Mashadi and S. Gemawati, Relationship of Lemoine Circle with A Symmedian Point, Journal of Mathematical Sciences, 17(2016) 23-33.

Keywords : Symmedian, area of symmedian triangle, side length of symmedian, trimedian, trisector.