X271

ISOGONAL CONJUGATE OF X208

X271 is the isogonal conjugate of X208.
< 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) { 8, 20 }: Central Line L(8, 20) { 200, 255 }: Central Line L(200, 255) { 78, 394 }: Central Line L(78, 394) { 282, 283 }: Central Line L(282, 283) { 2, 1034 }: Central Line L(2, 1034) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_8 = NAGEL POINT (0.4694, 0.1333) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_2 = CENTROID (0.5374, 0.2000) X_1034 = -CROSS CONJUGATE OF X(8) (0.3920, -0.4271) X_271 = ISOGONAL CONJUGATE OF X(208) (1.1546, 2.8606) A B C X208 X8 X20 X200 X255 X78 X394 X282 X283 X2 X1034 X271 (a, b, c) = (5, 6, 7) | AB = 1

X271 (ISOGONAL CONJUGATE OF X208) 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 \(f(A,B,C) = (\cot A \cot A/2)/(-1 - \cos A + \cos B + \cos C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(4.567076249114\)
▸ Incident Central Lines5 lines

{2, 1034}, {8, 20}, {78, 394}, {200, 255}, {282, 283}

▸ Functional Relations3 relations