X2128

EIGENTRANSFORM OF X19

X2128 = X19-Ceva conjugate of X63
< 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) { 63, 304 }: Central Line L(63, 304) { 1, 1958 }: Central Line L(1, 1958) { 2, 2082 }: Central Line L(2, 2082) { 19, 2129 }: Central Line L(19, 2129) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_19 = CLAWSON POINT (0.6246, 0.4244) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_1 = INCENTER (0.5714, 0.2333) X_1958 = CROSSSUM OF PU(23) (0.4653, 0.2026) X_2 = CENTROID (0.5374, 0.2000) X_2082 = NK-TRANSFORM OF X(9) (0.5920, 0.2164) X_2129 = ISOGONAL CONJUGATE OF X(2128) (0.9676, 0.4882) X_2128 = EIGENTRANSFORM OF X(19) (2.3357, 0.7428) A B C X19 X63 X304 X1 X1958 X2 X2082 X2129 X2128 (a, b, c) = (5, 6, 7) | AB = 1

X2128 (EIGENTRANSFORM OF X19) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b^{2} + c^{2} - a^{2})[(a^{2} + b^{2} + c^{2})^{2} - 8b^{2}c^{2}]\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(7.359138586080\)

X2128 lies on the cubic Z(X19).

▸ Incident Central Lines4 lines

{1, 1958}, {2, 2082}, {19, 2129}, {63, 304}

▸ Functional Relations2 relations