X2124

EIGENTRANSFORM OF X9

X2124 = X9-Ceva conjugate of X57
< 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) { 57, 279 }: Central Line L(57, 279) { 1, 971 }: Central Line L(1, 971) { 664, 728 }: Central Line L(664, 728) { 223, 1212 }: Central Line L(223, 1212) { 8, 2125 }: Central Line L(8, 2125) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2125 = ISOGONAL CONJUGATE OF X(2124) (0.8481, 4.0845) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_1 = INCENTER (0.5714, 0.2333) X_971 = INTERSECTION OF LINES X(3)X(9) AND X(4)X(7) (0.6441, 0.7770) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_728 = INTERSECTION OF LINES X(8)X(9) AND X(57)X(345) (0.3648, 0.0624) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_1212 = ISOGONAL CONJUGATE OF X(1170) (0.5256, 0.1789) X_8 = NAGEL POINT (0.4694, 0.1333) X_2124 = EIGENTRANSFORM OF X(9) (0.4700, -0.3153) A B C X2125 X57 X279 X1 X971 X664 X728 X223 X1212 X8 X2124 (a, b, c) = (5, 6, 7) | AB = 1

X2124 (EIGENTRANSFORM OF X9) 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 \(u : v : w\) = X9
Barycentrics: \(af(u,v,w) : bf(v,w,u) : cf(w,u,v)\)
Search Value (6, 9, 13): \(-0.621410268842\)

X2124 lies on the cubic K351.

▸ Incident Central Lines5 lines

{1, 971}, {8, 2125}, {57, 279}, {223, 1212}, {664, 728}

▸ Functional Relations4 relations