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(a) With usual notations, show that the circumcenter G of a triangle AABC is given in barycentric coordinates by G = (a² (b² + c² – a²) : b² (c² + a² – b²) : c² (a² + b² – c²)). (b) Show that the circumcenter of the triangle with vertices A(0,2), B(2,0), C(/2, V2) is the origin O(0,0).

(a) With usual notations, show that the circumcenter G of a triangle AABC is given in barycentric coordinates by G = (a² (b² + c² – a²) : b² (c² + a² – b²) : c² (a² + b² – c²)). (b) Show that the circumcenter of the triangle with vertices A(0,2), B(2,0), C(/2, V2) is the origin O(0,0).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Q3 (a) With usual notations, show that the circumcenter G of a triangle AABC is given in barycentric coordinates by G = (a² (b² + c² – a²) : b² (c² + a² – b²) : c² (a² + b² – c²)). (b) Show that the circumcenter of the triangle with vertices A(0,2), B(2,0), C(v2, v2) is the origin O(0,0).
Transcribed Image Text:Q3 (a) With usual notations, show that the circumcenter G of a triangle AABC is given in barycentric coordinates by G = (a² (b² + c² – a²) : b² (c² + a² – b²) : c² (a² + b² – c²)). (b) Show that the circumcenter of the triangle with vertices A(0,2), B(2,0), C(v2, v2) is the origin O(0,0).
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