X3450

1st SARAGOSSA POINT OF X8

X3450 = complementary conjugate of X3452
< 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) { 35, 572 }: Central Line L(35, 572) { 8, 1397 }: Central Line L(8, 1397) { 6, 1603 }: Central Line L(6, 1603) { 960, 1319 }: Central Line L(960, 1319) { 1193, 2003 }: Central Line L(1193, 2003) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4903, 0.1280) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_572 = ORTHOGONAL OF X(58) (0.5253, 0.1439) X_8 = NAGEL POINT (0.4694, 0.1333) X_1397 = -BETH CONJUGATE OF X(31) (0.6524, 0.4026) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1603 = TCC-PERSPECTOR OF X(8) (0.3539, -0.8165) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_1193 = 3rd SARAGOSSA POINT OF X(1) (0.5959, 0.2573) X_2003 = ORTHOCORRESPONDENT OF X(36) (0.5923, 0.2428) X_3450 = 1st SARAGOSSA POINT OF X(8) (0.6199, 0.3547) A B C X1329 X35 X572 X8 X1397 X6 X1603 X960 X1319 X1193 X2003 X3450 (a, b, c) = (5, 6, 7) | AB = 1

X3450 (1st SARAGOSSA POINT OF X8) 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 \(x : y : z\) = X8
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.173738165384\)
▸ 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)[\(a(b^{2}\) + \(c^{2})\) + (b + c)(b - c)2]} (E. Danneels)

▸ Incident Central Lines5 lines

{6, 1603}, {8, 1397}, {35, 572}, {960, 1319}, {1193, 2003}

▸ Functional Relations5 relations