X2187

X2-ISOCONJUGATE OF X189

X2187 = isogonal conjugate of X309
< 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) { 25, 41 }: Central Line L(25, 41) { 48, 55 }: Central Line L(48, 55) { 31, 184 }: Central Line L(31, 184) { 101, 200 }: Central Line L(101, 200) { 212, 692 }: Central Line L(212, 692) { 84, 947 }: Central Line L(84, 947) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_309 = ISOTOMIC CONJUGATE OF X(40) (0.6237, 0.7391) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_947 = ISOGONAL CONJUGATE OF X(946) (0.5457, 0.1609) X_2187 = -ISOCONJUGATE OF X(189) (0.5209, -0.0495) A B C X309 X25 X41 X48 X55 X31 X184 X101 X200 X212 X692 X84 X947 X2187 (a, b, c) = (5, 6, 7) | AB = 1

X2187 (X2-ISOCONJUGATE OF X189) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X189
Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)
Search Value (6, 9, 13): \(-2.135050367394\)
▸ Incident Central Lines13 lines

{25, 41}, {31, 184}, {40, 1817}, {48, 55}, {84, 947}, {101, 200}, {212, 692}, {228, 1253}, {601, 1437}, {968, 2268}, {1208, 1622}, {1458, 1473}, {1495, 2177}

▸ Functional Relations4 relations