X3348

ISOGONAL CONJUGATE OF X3183

X3348 is the isogonal conjugate of X3183.
< 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) { 2130, 3 }: Central Line L(2130, 3) { 20, 3183 }: Central Line L(20, 3183) { 1490, 3182 }: Central Line L(1490, 3182) { 4, 3355 }: Central Line L(4, 3355) { 40, 3353 }: Central Line L(40, 3353) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2130 = EIGENTRANSFORM OF X(20) (0.6000, 0.3192) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_3183 = -CEVA CONJUGATE OF X(4) (0.5835, 1.0296) X_1490 = ∩X(3)X(9) (0.3929, -0.4775) X_3182 = -CEVA CONJUGATE OF X(1) (0.5164, 5.7648) X_4 = ORTHOCENTER (0.6122, 0.3958) X_3355 = REFLECTION OF X(2131) IN X(3) (0.4675, 0.0474) X_40 = BEVAN POINT (0.4286, -0.0292) X_3353 = -CEVA CONJUGATE OF X(84) (0.6152, 0.5324) X_3348 = ISOGONAL CONJUGATE OF X(3183) (0.4000, -0.1150) A B C X2130 X3 X20 X3183 X1490 X3182 X4 X3355 X40 X3353 X3348 (a, b, c) = (5, 6, 7) | AB = 1

X3348 (ISOGONAL CONJUGATE OF X3183) 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 \(f(a,b,c) = 1/x : 1/y : 1/z\), where \(x : y : z\) = X3183
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.628930252649\)

X3348 lies on the Darboux cubic.

▸ Incident Central Lines6 lines

{1, 3472}, {3, 2130}, {4, 3355}, {20, 3183}, {40, 3353}, {1490, 3182}

▸ Functional Relations2 relations