X1055

POINT ALIOTH

X1055 = crosssum of X2 and X527
< 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) { 6, 41 }: Central Line L(6, 41) { 36, 101 }: Central Line L(36, 101) { 187, 237 }: Central Line L(187, 237) { 106, 919 }: Central Line L(106, 919) { 609, 995 }: Central Line L(609, 995) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1121 = -BLAIKIE TRANSFORM OF X(2) (0.8358, -0.1143) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_919 = ISOGONAL CONJUGATE OF X(918) (1.0058, 0.1699) X_609 = INTERSECTION OF LINES X(1)X(32) AND X(6)X(36) (0.6191, 0.3028) X_995 = MIDPOINT OF X(1) AND X(43) (0.6036, 0.2648) X_1055 = POINT ALIOTH (1.0459, 1.3483) A B C X1121 X6 X41 X36 X101 X187 X237 X106 X919 X609 X995 X1055 (a, b, c) = (5, 6, 7) | AB = 1

X1055 (POINT ALIOTH) 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 \(f(a,b,c) = a(b^{2} + c^{2} - 2a^{2} + ab + ac - 2bc)\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-1.418739090767\)
▸ Incident Central Lines5 lines

{6, 41}, {36, 101}, {106, 919}, {187, 237}, {609, 995}

▸ Functional Relations5 relations