X3440

X15-VERTEX CONJUGATE OF X15

X3440 = isogonal conjugate of X616
< 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) { 30, 298 }: Central Line L(30, 298) { 15, 1495 }: Central Line L(15, 1495) { 399, 1338 }: Central Line L(399, 1338) { 2132, 3441 }: Central Line L(2132, 3441) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_3441 = -VERTEX CONJUGATE OF X(16) (-0.3191, 0.5552) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_1495 = CROSSSUM OF X(2) AND X(30) (0.8194, 1.4855) X_399 = PARRY REFLECTION POINT (0.0032, 0.9936) X_1338 = 2nd WERNAU POINT (1.0969, 0.1421) X_2132 = EIGENTRANSFORM OF X(30) (1.2703, 0.4856) X_3440 = -VERTEX CONJUGATE OF X(15) (0.6192, 0.5141) A B C X74 X3441 X30 X298 X15 X1495 X399 X1338 X2132 X3440 (a, b, c) = (5, 6, 7) | AB = 1

X3440 (X15-VERTEX CONJUGATE OF X15) 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 \(f(a,b,c) = a/[a^{2}vwyz - ux(bw + cv)(bz + cy)]\), where \(u : v : w\) = X15 and \(x : y : z\) = X15
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-5.041013046022\)

X3440 lies on the Neuberg cubic.

▸ Incident Central Lines4 lines

{15, 1495}, {30, 298}, {399, 1338}, {2132, 3441}

▸ Functional Relations2 relations