X3566

2nd MOSES INFINITY POINT

X3566 = crossdifference of every pair of points on line X6X1196
< 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) { 30, 511 }: Central Line L(30, 511) { 64, 879 }: Central Line L(64, 879) { 1640, 1853 }: Central Line L(1640, 1853) { 669, 3265 }: Central Line L(669, 3265) { 2489, 2506 }: Central Line L(2489, 2506) { 2491, 2524 }: Central Line L(2491, 2524) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3565 = 2nd MOSES CIRCUMCIRCLE POINT (0.0672, -0.1683) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_879 = ISOTOMIC CONJUGATE OF X(877) (1.2088, 0.0345) X_1640 = TRIPOLAR CENTROID OF X(98) (0.8552, 0.1697) X_1853 = ZOSMA TRANSFORM OF X(204) (0.5941, 0.7953) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_3265 = ISOTOMIC CONJUGATE OF X(107) (-2.4538, 0.0692) X_2489 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE CIRCLE} (0.1726, 0.9764) X_2506 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, 2nd LEMOINE CIRCLE} (0.4241, 0.3737) X_2491 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, GALLATLY CIRCLE} (1.0687, 0.6339) X_2524 = RADICAL CENTER OF {NINE-POINT, BROCARD, 2nd BROCARD} CIRCLES (1.4600, -0.3036) X_3566 = 2nd MOSES INFINITY POINT (0.7634, -0.3416) A B C X3565 X30 X511 X64 X879 X1640 X1853 X669 X3265 X2489 X2506 X2491 X2524 X3566 (a, b, c) = (5, 6, 7) | AB = 1

X3566 (2nd MOSES INFINITY POINT) 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 \(f(a,b,c) = bc(3a^{2} - b^{2} - c^{2})(b^{2} - c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
▸ Incident Central Lines8 lines

{30, 511}, {64, 879}, {669, 3265}, {1640, 1853}, {2088, 3143}, {2489, 2506}, {2491, 2524}, {2450, 3569}

▸ Functional Relations4 relations