X1079

TRILINEAR SQUARE OF X46

< 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, 4 }: Incenter–Orthocenter Line { 77, 498 }: Central Line L(77, 498) { 651, 920 }: Central Line L(651, 920) { 46, 1406 }: Central Line L(46, 1406) { 484, 1103 }: Central Line L(484, 1103) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_920 = -CEVA CONJUGATE OF X(1) (0.8006, 0.5344) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_1406 = -BETH CONJUGATE OF X(46) (0.6653, 0.5088) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_1103 = TRILINEAR SQUARE OF X(40) (0.3353, 0.0019) X_1079 = TRILINEAR SQUARE OF X(46) (0.6490, 0.5422) A B C X1 X4 X77 X498 X651 X920 X46 X1406 X484 X1103 X1079 (a, b, c) = (5, 6, 7) | AB = 1

X1079 (TRILINEAR SQUARE OF X46) 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 \(f(A,B,C) = (\cos B + \cos C - \cos A)^{2}\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(0.260138704563\)
▸ Incident Central Lines5 lines

{1, 4}, {46, 1406}, {77, 498}, {484, 1103}, {651, 920}