PENGEMBANGAN TEOREMA SAWAYAMA-THEBAULT MENGGUNAKAN EXCENTER - Surlina Surlina; Mashadi Mashadi; Sri Gemawati (Universitas Asahan, 2018)
AbstractA triangle have special lines, such as angle bisectors and perpendicular bisector.These special lines are concurrent with their corresponding concurrent points, and called incenter, excenter and circumcenter. This paper discusses how to prove the collinear point of Sawayama-Thebault’s circle using excenter. Then, it is proved the three points collinear using simple ways, like similarity triangles and Thales theorem.Keywords: Sawayama-Thebault’s theorem, excenter, collinearAbstrakSegitiga memiliki beberapa garis-garis istimewa, diantaranya garis bagi, dan garis sumbu. Garis-garis istimewa ini kongkuren dan masing-masing titik kongkuren disebut incenter, excenter dan circumcenter . Pada makalah ini dibahas kolinearitas titik pusat lingkaran Sawayama-Thebault menggunakan excenter. Pembuktian kekolinearitas menggunakan konsep geometri sederhana, yakni kesebangunan segitiga dan teorema Thales.Kata kunci: Teorema Sawayama-Thebault, excenter, kolinearitas