X3489

ISOGONAL CONJUGATE OF X627

X3489 is the isogonal conjugate of X627.
< 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) { 51, 61 }: Central Line L(51, 61) { 5, 302 }: Central Line L(5, 302) { 3, 1337 }: Central Line L(3, 1337) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_3490 = ISOGONAL CONJUGATE OF X(628) (0.2382, 0.0845) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_302 = ISOTOMIC CONJUGATE OF 1st NAPOLEON POINT (0.5043, 0.1643) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1337 = 1st WERNAU POINT (2.6910, 4.6498) X_3489 = ISOGONAL CONJUGATE OF X(627) (0.6244, 0.3603) A B C X54 X3490 X51 X61 X5 X302 X3 X1337 X3489 (a, b, c) = (5, 6, 7) | AB = 1

X3489 (ISOGONAL CONJUGATE OF X627) 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 \(f(a,b,c) = 1/x(627)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.627378260946\)

X3489 lies on the Napoleon cubic.

▸ Incident Central Lines3 lines

{3, 1337}, {5, 302}, {51, 61}

▸ Functional Relations2 relations