X3354

ISOGONAL CONJUGATE OF X3353

X3354 is the isogonal conjugate of X3353.
< 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) { 3472, 3 }: Central Line L(3472, 3) { 40, 2130 }: Central Line L(40, 2130) { 20, 3353 }: Central Line L(20, 3353) { 1490, 3183 }: Central Line L(1490, 3183) { 1498, 3182 }: Central Line L(1498, 3182) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3472 = -CEVA CONJUGATE OF X(3345) (0.5432, 0.1758) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_40 = BEVAN POINT (0.4286, -0.0292) X_2130 = EIGENTRANSFORM OF X(20) (0.6000, 0.3192) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_3353 = -CEVA CONJUGATE OF X(84) (0.6152, 0.5324) X_1490 = ∩X(3)X(9) (0.3929, -0.4775) X_3183 = -CEVA CONJUGATE OF X(4) (0.5835, 1.0296) X_1498 = REFLECTION OF X(64) IN X(3) (0.4421, -1.3902) X_3182 = -CEVA CONJUGATE OF X(1) (0.5164, 5.7648) X_3354 = ISOGONAL CONJUGATE OF X(3353) (0.4568, 0.0283) A B C X3472 X3 X40 X2130 X20 X3353 X1490 X3183 X1498 X3182 X3354 (a, b, c) = (5, 6, 7) | AB = 1

X3354 (ISOGONAL CONJUGATE OF X3353) 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 \(f(a,b,c) = 1/x(3353)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-12.223061551055\)

X3354 lies on the Darboux cubic.

▸ Incident Central Lines6 lines

{1, 3355}, {3, 3472}, {20, 3353}, {40, 2130}, {1490, 3183}, {1498, 3182}

▸ Functional Relations3 relations