X3449

1st SARAGOSSA POINT OF X7

Saragossa points are discussed just before X1166.
< 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) { 572, 672 }: Central Line L(572, 672) { 6, 1602 }: Central Line L(6, 1602) { 7, 2175 }: Central Line L(7, 2175) { 518, 2330 }: Central Line L(518, 2330) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2175 = -ISOCONJUGATE OF X(85) (0.6102, 0.2574) X_572 = ORTHOGONAL OF X(58) (0.5253, 0.1439) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_1602 = TCC-PERSPECTOR OF X(7) (0.5590, 0.3060) X_7 = GERGONNE POINT (0.5903, 0.2769) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_2330 = -ISOCONJUGATE OF X(1432) (0.5612, 0.2101) X_3449 = 1st SARAGOSSA POINT OF X(7) (0.6052, 0.2623) A B C X6 X2175 X572 X672 X1602 X7 X518 X2330 X3449 (a, b, c) = (5, 6, 7) | AB = 1

X3449 (1st SARAGOSSA POINT OF X7) 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 \(x : y : z\) = X7
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(1.022521519399\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines4 lines

{6, 1602}, {7, 2175}, {518, 2330}, {572, 672}

▸ Functional Relations3 relations