X3481

INTERSECTION OF LINES X3X_2120 and X4X_2121

X3481 = isogonal conjugate of X3482
< 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) { 3, 2120 }: Central Line L(3, 2120) { 4, 2121 }: Central Line L(4, 2121) { 30, 3482 }: Central Line L(30, 3482) { 3465, 3483 }: Central Line L(3465, 3483) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3482 = ISOGONAL CONJUGATE OF X(3481) (0.2339, -0.0437) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2120 = EIGENTRANSFORM OF X(5) (0.5135, 0.2811) X_4 = ORTHOCENTER (0.6122, 0.3958) X_2121 = ISOGONAL CONJUGATE OF X(2120) (0.6451, 0.1816) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_3465 = -CEVA CONJUGATE OF X(484) (-0.1212, -2.5237) X_3483 = INTERSECTION OF LINES X(1)X(1157) and X(4)X(484) (0.3928, 0.0056) X_3481 = INTERSECTION OF LINES X(3)X(2120) and X(4)X(2121) (0.5519, 0.7884) A B C X3482 X3 X2120 X4 X2121 X30 X3465 X3483 X3481 (a, b, c) = (5, 6, 7) | AB = 1

X3481 (INTERSECTION OF LINES X3X_2120 and X4X_2121) 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 \(f(a,b,c) = P + Q + (16Px + P^{2} + 4PQ + 3Q^{2} - 24P)/(8x^{2} - 8x + P + 7Q)\), where \(P = 16S^{2}/(a + b + c)^{4}\), \(Q = -1 + 4(bc + ca + ab)/(a + b + c)^{2}\), \(S = 2(\operatorname{area} of ABC)\); and \(x = (-a + b + c)/(a + b + c)\) (M. Iliev, 10/27/08)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.910588404776\)

X3481 lies on the Neuberg cubic.

▸ Incident Central Lines4 lines

{3, 2120}, {4, 2121}, {30, 3482}, {3465, 3483}

▸ Functional Relations1 relation