X3451

1st SARAGOSSA POINT OF X9

X3451 = X667-cross conjugate of X109
< 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) { 9, 604 }: Central Line L(9, 604) { 55, 572 }: Central Line L(55, 572) { 6, 1604 }: Central Line L(6, 1604) { 284, 1404 }: Central Line L(284, 1404) { 333, 1412 }: Central Line L(333, 1412) { 1108, 2161 }: Central Line L(1108, 2161) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3452 = ISOGONAL CONJUGATE OF X(3451) (0.4992, 0.1444) X_9 = MITTENPUNKT (0.5110, 0.1615) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_572 = ORTHOGONAL OF X(58) (0.5253, 0.1439) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1604 = TCC-PERSPECTOR OF X(9) (0.3886, -0.5005) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_1404 = -BETH CONJUGATE OF X(44) (0.8219, 0.8053) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_1412 = -BETH CONJUGATE OF X(81) (0.6374, 0.3603) X_1108 = CROSSPOINT OF X(2) AND X(84) (0.6346, 0.3084) X_2161 = -ISOCONJUGATE OF X(36) (0.9328, -0.1235) X_3451 = 1st SARAGOSSA POINT OF X(9) (0.6180, 0.3325) A B C X3452 X9 X604 X55 X572 X6 X1604 X284 X1404 X333 X1412 X1108 X2161 X3451 (a, b, c) = (5, 6, 7) | AB = 1

X3451 (1st SARAGOSSA POINT OF X9) 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 \(f(a,b,c) = a/(x(bz + cy)\), where \(x : y : z\) = X9
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.257209630594\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a/\){(b + c - a)[a(b + c) + (b - c)2]} (E. Danneels)

▸ Incident Central Lines8 lines

{6, 1604}, {9, 604}, {55, 572}, {284, 1404}, {333, 1412}, {1108, 2161}, {1400, 2316}, {2259, 2317}

▸ Functional Relations4 relations