X3268

ISOTOMIC CONJUGATE OF X476

X3268 is the isotomic conjugate of X476.
< 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) { 99, 110 }: Central Line L(99, 110) { 325, 523 }: Central Line L(325, 523) { 2, 1637 }: Central Line L(2, 1637) { 525, 1636 }: Central Line L(525, 1636) { 147, 2793 }: Central Line L(147, 2793) { 339, 2972 }: Central Line L(339, 2972) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_476 = TIXIER POINT (0.9824, 0.2685) X_99 = STEINER POINT (0.1109, 0.4322) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_2 = CENTROID (0.5374, 0.2000) X_1637 = TRIPOLAR CENTROID OF X(4) (1.3086, 0.5422) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_1636 = TRIPOLAR CENTROID OF X(3) (-3.1554, -0.2797) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_2793 = ISOGONAL CONJUGATE OF X(2709) (0.2567, -0.3154) X_339 = ISOTOMIC CONJUGATE OF X(250) (0.6002, 0.0170) X_2972 = 6th MACBEATH POINT (0.5552, 0.0030) X_3268 = ISOTOMIC CONJUGATE OF X(476) (-1.0050, -0.4845) A B C X476 X99 X110 X325 X523 X2 X1637 X525 X1636 X147 X2793 X339 X2972 X3268 (a, b, c) = (5, 6, 7) | AB = 1

X3268 (ISOTOMIC CONJUGATE OF X476) 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 \(f(A,B,C) = (\csc^{2} A)(\sin(B - C))(1 + 2 \cos 2A)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(14.105454272420\)
▸ Incident Central Lines8 lines

{2, 1637}, {99, 110}, {147, 2793}, {325, 523}, {339, 2972}, {525, 1636}, {1297, 2373}, {2394, 2986}

▸ Functional Relations7 relations