CD Tesis

Pengembangan Teorema Sawayama-Thebault Menggunakan Excenter

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A triangle has 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 thesis discusses how to compute the radian of Sawayama-Thebault’s circle using trigonometry and area of a triangle, i.e. r1 = (L/a)(1 − βτ )(1 + γτ ) and r2 = (L/aτ 2)(τ + β)(τ − γ). Notation L is area of ΔABC , β = tan(A/2), γ = tan(C/2), and τ = 2θ = 2∠AT B. Proof of collinear point of Sawayama-Thebault’s circle is carried out using similarity triangles and Thales’ theorem. Meanwhile, the relationship amongst the radians R1, R2 and Ra of Sawayama-Thebault using excenter is given by Ra = (R1 sin2 θ + R2 cos2 θ).
Keywords: Sawayama-Thebault’s theorem, excenter, circumcenter, collinear

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

10 15. 218 (0003)

Penerbit

Pekanbaru : Universitas Riau – Pasca Sarjana – Tesis Matematika., 2018

Deskripsi Fisik

xii, 59 hlm.; ill.; 29 cm

Bahasa

Indonesia

ISBN/ISSN

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Klasifikasi

10 15. 218 (0003)

Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

PASCASARJANA (MAGISTER) MATEMATIKA

Info Detail Spesifik

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Pernyataan Tanggungjawab

FATAH

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