PENGEMBANGAN TEOREMA DAO PADA ENAM CIRCUMCENTER
DOI:
https://doi.org/10.33603/e.v5i1.514Abstrak
Dalam tulisan ini diberikan pengembangan dari Teorema Dao pada enam circumcenter yang terhubung dengan segienam siklis yang membentuk dua pasang segitiga orthologic dengan titik pusat orthologic-nya sama dengan titik pusat lingkaran awal. Pembuktian dari pengembangan teorema ini dilakukan dengan menggunakan konsep sederhana yang dapat dipahami oleh siswa sekolah menengah, yaitu konsep kekongruenan.
Kata Kunci: Teorema Dao, circumcenter, segitiga orthologic.
Referensi
DAFTAR PUSTAKA
Cerin, Zvanko. (1997). Hyperbolas and orthologic triangles, Mathematica Pannonica, 8; 201-214.
Cerin, Zvanko. (2010). Rings of Squares around orthologic triangles, Forum Geometricorum 9; 57-80.
Cohl, Telv. (2014). A purely synthetic proof of Dao’s theorem on six circumcenters associated with a cyclic hexagon, Forum Geometricorum 2014; 14; 261-264.
Dergiades, Nikolas. (2014). Dao’s theorem on six circumcenters associated with a cyclic hexagon, Forum Geometricorum 2014; 14; 243-246.
Duong, N. Q. (2016). Some problems around the Dao’s theorem on six circumcenters associated with a cyclic hexagon configuration, The International Journal of Computer Discovered Mathematics 2016; 1; 40-47.
Joyce, D. E. (1996). Euclid’s Elements, Department of Mathematics and Computer Science Clark University, Worcester.
Mashadi. (2012). Geometri. Pekanbaru: Pusbangdik Universitas Riau.
Mashadi. (2015). Geometri Lanjut. Pekanbaru: Universitas Riau Press.
Mashadi, Gemawati, S., Hasriati dan Herlinawati, S. (2015). Semi-Excircle of Quadrilateral, JP Journal of Mathematical Sciences, 15; 1-13.
Mashadi, Valentika, C., dan Gemawati, S. (2017). Development of Napoleon’s Theorem on the Rectanglesin Case of Inside Direction, International Journal of Theoretical and Applied Mathematics, 3(2): 54-57.
Patrascu, I., dan Smarandache, F. (2010[a]). A Theorem about Simultaneous Orthological and Homological Triangles, Smarandhace Nations Journal; 1; 1-13.
Patrascu, I., dan Smarandache, F. (2010[b]). Pantazi’s theorem regarding the bi-orthological triangles, Smarandhace Nations Journal; 1; 1-5.
Valentika, C., Mashadi, dan Gemawati, S. (2016). The Development Of Napoleon’s Theorem On Quadrilateral With Congruence And Trigonometry, Bulletin of Mathematics 2016; 8; 97–108.
Zukrianto, Mashadi, dan Gemawati, S. (2016). A nonconvex quadrilateral and Semi Georgonne Points on it: some results and analysis, Fundamental Journal of Mathematics and Mathematical Sciences 2016, 6; 111-124.
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