X2131

ISOGONAL CONJUGATE OF X2130

X2131 is the isogonal conjugate of X2130.
< 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) { 3355, 3 }: Central Line L(3355, 3) { 20, 2130 }: Central Line L(20, 2130) { 40, 3472 }: Central Line L(40, 3472) { 1498, 3183 }: Central Line L(1498, 3183) { 1490, 3353 }: Central Line L(1490, 3353) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3355 = REFLECTION OF X(2131) IN X(3) (0.4675, 0.0474) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_2130 = EIGENTRANSFORM OF X(20) (0.6000, 0.3192) X_40 = BEVAN POINT (0.4286, -0.0292) X_3472 = -CEVA CONJUGATE OF X(3345) (0.5432, 0.1758) X_1498 = REFLECTION OF X(64) IN X(3) (0.4421, -1.3902) X_3183 = -CEVA CONJUGATE OF X(4) (0.5835, 1.0296) X_1490 = ∩X(3)X(9) (0.3929, -0.4775) X_3353 = -CEVA CONJUGATE OF X(84) (0.6152, 0.5324) X_2131 = ISOGONAL CONJUGATE OF X(2130) (0.5325, 0.1568) A B C X3355 X3 X20 X2130 X40 X3472 X1498 X3183 X1490 X3353 X2131 (a, b, c) = (5, 6, 7) | AB = 1

X2131 (ISOGONAL CONJUGATE OF X2130) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(u,v,w) : 1/f(v,w,u) : 1/f(w,u,v)\), where f is as given just before X2120 and \(u : v : w\) = X20
Barycentrics: \(a/f(u,v,w) : b/f(v,w,u) : c/f(w,u,v)\)
Search Value (6, 9, 13): \(183.441471170582\)

X2131 lies on the Darboux cubic (K004).

▸ Incident Central Lines5 lines

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

▸ Functional Relations3 relations