X261

ISOTOMIC CONJUGATE OF X12

X261 is the isotomic conjugate of X12.
< 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) { 58, 86 }: Central Line L(58, 86) { 75, 99 }: Central Line L(75, 99) { 28, 242 }: Central Line L(28, 242) { 21, 314 }: Central Line L(21, 314) { 272, 310 }: Central Line L(272, 310) { 2, 593 }: Central Line L(2, 593) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_99 = STEINER POINT (0.1109, 0.4322) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_242 = -LINE CONJUGATE OF X(71) (0.7507, 0.7161) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_272 = ISOGONAL CONJUGATE OF X(209) (-0.2458, -0.0534) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_2 = CENTROID (0.5374, 0.2000) X_593 = 1st HATZIPOLAKIS-YIU POINT (0.6202, 0.3026) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) A B C X12 X58 X86 X75 X99 X28 X242 X21 X314 X272 X310 X2 X593 X261 (a, b, c) = (5, 6, 7) | AB = 1

X261 (ISOTOMIC CONJUGATE OF X12) 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 \(f(A,B,C) = [(\csc A)(\sec(B/2 - C/2))]^{2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.744047967075\)
▸ Incident Central Lines12 lines

{2, 593}, {9, 645}, {21, 314}, {28, 242}, {58, 86}, {75, 99}, {272, 310}, {284, 332}, {317, 406}, {319, 502}, {552, 873}, {572, 662}

▸ Functional Relations7 relations