X1103

TRILINEAR SQUARE OF X40

X1103 = isogonal conjugate of X1256
< 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, 2 }: Nagel Line { 40, 221 }: Central Line L(40, 221) { 46, 269 }: Central Line L(46, 269) { 165, 255 }: Central Line L(165, 255) { 31, 937 }: Central Line L(31, 937) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1256 = ISOGONAL CONJUGATE OF X(1103) (0.6135, 0.5942) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_40 = BEVAN POINT (0.4286, -0.0292) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_937 = ISOGONAL CONJUGATE OF X(936) (0.6143, 0.2920) X_1103 = TRILINEAR SQUARE OF X(40) (0.3353, 0.0019) A B C X1256 X1 X2 X40 X221 X46 X269 X165 X255 X31 X937 X1103 (a, b, c) = (5, 6, 7) | AB = 1

X1103 (TRILINEAR SQUARE OF X40) 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 \(f(A,B,C) = (\cos B + \cos C - \cos A - 1)^{2}\)
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): \(2.402196688599\)
▸ Incident Central Lines5 lines

{1, 2}, {31, 937}, {40, 221}, {46, 269}, {165, 255}

▸ Functional Relations1 relation