X3465

X30-CEVA CONJUGATE OF X484

X3465 = reflection of X484 in X2222
< 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) { 484, 2222 }: Central Line L(484, 2222) { 1, 4 }: Incenter–Orthocenter Line { 35, 228 }: Central Line L(35, 228) { 74, 484 }: Central Line L(74, 484) { 36, 1736 }: Central Line L(36, 1736) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_2222 = -ISOCONJUGATE OF X(654) (0.9870, 0.2545) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_228 = -CEVA CONJUGATE OF X(71) (0.5231, 0.1126) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1736 = MIMOSA TRANSFORM OF X(103) (1.0370, 0.7863) X_3465 = -CEVA CONJUGATE OF X(484) (-0.1212, -2.5237) A B C X484 X2222 X1 X4 X35 X228 X74 X36 X1736 X3465 (a, b, c) = (5, 6, 7) | AB = 1

X3465 (X30-CEVA CONJUGATE OF X484) 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 \(f(a,b,c) = x(- x/u + y/v + z/w)\), where \(u : v : w\) = X5,\(x : y : z\) = X484
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.156173581549\)

X3465 lies on the Neuberg cubic.

▸ Incident Central Lines12 lines

{1, 4}, {30, 1807}, {35, 228}, {36, 1736}, {74, 484}, {108, 2732}, {912, 1936}, {1047, 1048}, {1157, 3065}, {1725, 1758}, {2250, 2341}, {3481, 3483}

▸ Functional Relations6 relations