X2122

EIGENTRANSFORM OF X8

X2122 = X8-Ceva conjugate of X56
< 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) { 1, 84 }: Central Line L(1, 84) { 109, 1035 }: Central Line L(109, 1035) { 34, 1767 }: Central Line L(34, 1767) { 608, 1249 }: Central Line L(608, 1249) { 603, 1450 }: Central Line L(603, 1450) { 1406, 1456 }: Central Line L(1406, 1456) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1 = INCENTER (0.5714, 0.2333) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_1035 = ISOGONAL CONJUGATE OF X(1034) (0.4590, -14.0277) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_1767 = MIMOSA TRANSFORM OF X(347) (2.7220, 22.3050) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_1249 = ISOGONAL CONJUGATE OF X(1073) (-0.9482, -15.9845) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_1450 = -BETH CONJUGATE OF X(392) (0.6088, 0.2886) X_1406 = -BETH CONJUGATE OF X(46) (0.6653, 0.5088) X_1456 = -BETH CONJUGATE OF X(516) (0.7238, 1.0576) X_2122 = EIGENTRANSFORM OF X(8) (0.3815, -2.1505) A B C X8 X56 X1 X84 X109 X1035 X34 X1767 X608 X1249 X603 X1450 X1406 X1456 X2122 (a, b, c) = (5, 6, 7) | AB = 1

X2122 (EIGENTRANSFORM OF X8) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(u,v,w) : f(v,w,u) : f(w,u,v)\), where f is as given just before X2120 and \(u : v : w\) = X8
Barycentrics: \(af(u,v,w) : bf(v,w,u) : cf(w,u,v)\)
Search Value (6, 9, 13): \(-0.249226860735\)

X2122 lies on the cubic K692.

▸ Incident Central Lines7 lines

{1, 84}, {8, 2123}, {34, 1767}, {109, 1035}, {603, 1450}, {608, 1249}, {1406, 1456}

▸ Functional Relations2 relations