X260

ISOGONAL CONJUGATE OF X177

X260 is the isogonal conjugate of X177.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 259, 266 }: Central Line L(259, 266) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_259 = ISOGONAL CONJUGATE OF X(174) (0.5606, 0.2123) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_266 = ISOGONAL CONJUGATE OF X(188) (0.6074, 0.2891) X_260 = ISOGONAL CONJUGATE OF X(177) (0.5546, 0.2025) A B C X55 X259 X1 X3 X266 X260 (a, b, c) = (5, 6, 7) | AB = 1

X260 (ISOGONAL CONJUGATE OF X177) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (\cos A/2)/(\cos B/2 + \cos C/2)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.408684354404\)
▸ Incident Central Lines2 lines

{1, 3}, {259, 266}

▸ Functional Relations2 relations