X189

CYCLOCEVIAN CONJUGATE OF X8

X189 is the perspector of triangle ABC and the pedal triangle of X84.
< 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) { 2, 77 }: Central Line L(2, 77) { 7, 92 }: Central Line L(7, 92) { 29, 81 }: Central Line L(29, 81) { 69, 309 }: Central Line L(69, 309) { 222, 281 }: Central Line L(222, 281) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_8 = NAGEL POINT (0.4694, 0.1333) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_2 = CENTROID (0.5374, 0.2000) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_7 = GERGONNE POINT (0.5903, 0.2769) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_309 = ISOTOMIC CONJUGATE OF X(40) (0.6237, 0.7391) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_189 = CYCLOCEVIAN CONJUGATE OF X(8) (0.6131, 0.7055) A B C X198 X8 X20 X2 X77 X7 X92 X29 X81 X69 X309 X222 X281 X189 (a, b, c) = (5, 6, 7) | AB = 1

X189 (CYCLOCEVIAN CONJUGATE OF X8) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc/(\cos B + \cos C - \cos A - 1) : ca/(\cos C + \cos A - \cos B - 1) : ab/(\cos A + \cos B - \cos C - 1)\)
Barycentrics: \(1/(\cos B + \cos C - \cos A - 1) : 1/(\cos C + \cos A - \cos B - 1) : 1/(\cos A + \cos B - \cos C - 1)\)
Search Value (6, 9, 13): \(9.489626975767\)

X189 lies on the Lucas cubic.

▸ Incident Central Lines6 lines

{2, 77}, {7, 92}, {8, 20}, {29, 81}, {69, 309}, {222, 281}

▸ Functional Relations9 relations