X2138

EIGENTRANSFORM OF X69

X2138 = X69-Ceva conjugate of X25
< 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) { 6, 64 }: Central Line L(6, 64) { 1249, 1941 }: Central Line L(1249, 1941) { 69, 2139 }: Central Line L(69, 2139) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_1249 = ISOGONAL CONJUGATE OF X(1073) (-0.9482, -15.9845) X_1941 = CROSSSUM OF PU(17) (0.5282, 0.3794) X_2139 = ISOGONAL CONJUGATE OF X(2138) (0.3817, -0.0947) X_2138 = EIGENTRANSFORM OF X(69) (0.5787, 0.9388) A B C X69 X25 X6 X64 X1249 X1941 X2139 X2138 (a, b, c) = (5, 6, 7) | AB = 1

X2138 (EIGENTRANSFORM OF X69) 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 \(u : v : w\) = X69
Barycentrics: \(af(u,v,w) : bf(v,w,u) : cf(w,u,v)\)
Search Value (6, 9, 13): \(0.382101333784\)

X2138 lies on the cubic K169.

▸ Incident Central Lines3 lines

{6, 64}, {69, 2139}, {1249, 1941}

▸ Functional Relations2 relations