X3490

ISOGONAL CONJUGATE OF X628

X3490 is the isogonal conjugate of X628.
< 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, 62 }: Central Line L(51, 62) { 5, 303 }: Central Line L(5, 303) { 3, 1338 }: Central Line L(3, 1338) 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_3489 = ISOGONAL CONJUGATE OF X(627) (0.6244, 0.3603) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_303 = ISOTOMIC CONJUGATE OF 2nd NAPOLEON POINT (0.6079, 0.2757) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1338 = 2nd WERNAU POINT (1.0969, 0.1421) X_3490 = ISOGONAL CONJUGATE OF X(628) (0.2382, 0.0845) A B C X54 X3489 X51 X62 X5 X303 X3 X1338 X3490 (a, b, c) = (5, 6, 7) | AB = 1

X3490 (ISOGONAL CONJUGATE OF X628) 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 \(f(a,b,c) = 1/x(628)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.014239703304\)

X3490 lies on the Napoleon cubic.

▸ Incident Central Lines3 lines

{3, 1338}, {5, 303}, {51, 62}

▸ Functional Relations2 relations