X3484

INTERSECTION OF LINES X3X_2120 and X4X_54

X3484 is the tangential of X4 on the Neuberg cubic.
< 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) { 4, 54 }: Central Line L(4, 54) { 74, 1157 }: Central Line L(74, 1157) { 3, 2120 }: Central Line L(3, 2120) { 484, 3466 }: Central Line L(484, 3466) { 3479, 3480 }: Central Line L(3479, 3480) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (1.5871, 1.5280) X_4 = ORTHOCENTER (0.6122, 0.3958) X_54 = KOSNITA POINT (0.5880, 0.2176) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2120 = EIGENTRANSFORM OF X(5) (0.5135, 0.2811) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_3466 = ISOGONAL CONJUGATE OF X(3465) (0.6227, -0.5773) X_3479 = ISOGONAL CONJUGATE OF X(1337) (0.8262, -0.2295) X_3480 = ISOGONAL CONJUGATE OF X(1338) (1.4651, 1.1054) X_3484 = INTERSECTION OF LINES X(3)X(2120) and X(4)X(54) (0.4090, -1.1012) A B C X30 X1157 X4 X54 X74 X3 X2120 X484 X3466 X3479 X3480 X3484 (a, b, c) = (5, 6, 7) | AB = 1

X3484 (INTERSECTION OF LINES X3X_2120 and X4X_54) 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 \(f(a,b,c) = a[4x^{2} - 5y^{2} - 5z^{2} + 2xy + 2xz + 10yz - (y + z)(3y + z)(y + 3z)/(2x + y + z)]\), where x : y : \(z = 1/(b^{2} + c^{2} - a^{2}) : 1/(c^{2} + a^{2} - b^{2}) : 1/(a^{2} + b^{2} - c^{2})\) (M. Iliev, 10/27/08)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-5.838288208608\)

X3484 lies on the Neuberg cubic, then circle {{X4,X15,X16,X186}}.

▸ Incident Central Lines5 lines

{3, 2120}, {4, 54}, {74, 1157}, {484, 3466}, {3479, 3480}

▸ Functional Relations2 relations