X3470

TRILINEAR PRODUCT X74*X1749

X3470 = X2914-cross conjugate of X1157
< 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) { 3, 74 }: Central Line L(3, 74) { 5, 1117 }: Central Line L(5, 1117) { 1138, 2132 }: Central Line L(1138, 2132) { 3459, 3462 }: Central Line L(3459, 3462) { 3467, 3468 }: Central Line L(3467, 3468) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2914 = ORTHIC-ISOGONAL CONJUGATE OF X(186) (0.5079, 0.4982) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (1.5871, 1.5280) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1117 = POINT ALRESCHA (0.9978, 0.0022) X_1138 = ISOGONAL CONJUGATE OF X(399) (-0.2714, 0.2752) X_2132 = EIGENTRANSFORM OF X(30) (1.2703, 0.4856) X_3459 = ISOGONAL CONJUGATE OF X(195) (0.3786, 0.1244) X_3462 = -CEVA CONJUGATE OF X(4) (0.4603, -0.7229) X_3467 = ISOGONAL CONJUGATE OF X(3336) (0.4625, 0.1294) X_3468 = -CEVA CONJUGATE OF X(3336) (0.5161, 0.0130) X_3470 = TRILINEAR PRODUCT X(74)*X(1749) (0.3559, 0.3608) A B C X2914 X1157 X3 X74 X5 X1117 X1138 X2132 X3459 X3462 X3467 X3468 X3470 (a, b, c) = (5, 6, 7) | AB = 1

X3470 (TRILINEAR PRODUCT X74*X1749) 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 \(f(a,b,c) = x(74)x(1749)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.977359009850\)

X3470 lies on the Napoleon cubic.

▸ Incident Central Lines5 lines

{3, 74}, {5, 1117}, {1138, 2132}, {3459, 3462}, {3467, 3468}

▸ Functional Relations3 relations