X3453

1st SARAGOSSA POINT OF X10

X3453 = X1324-cross conjugate of X759
< 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) { 60, 386 }: Central Line L(60, 386) { 404, 849 }: Central Line L(404, 849) { 261, 1078 }: Central Line L(261, 1078) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3454 = ISOGONAL CONJUGATE OF X(3453) (0.5008, 0.1575) X_60 = ISOGONAL CONJUGATE OF X(12) (0.5790, 0.2258) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_849 = 4th HATZIPOLAKIS-YIU POINT (0.6376, 0.3351) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_1078 = INTERSECTION OF LINES X(2)X(32) AND X(3)X(76) (0.4771, 0.1215) X_3453 = 1st SARAGOSSA POINT OF X(10) (0.6194, 0.3150) A B C X3454 X60 X386 X404 X849 X261 X1078 X3453 (a, b, c) = (5, 6, 7) | AB = 1

X3453 (1st SARAGOSSA POINT OF X10) 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 \(x : y : z\) = X10
Barycentrics: \(ag(a,b,c) : bg(b,c,a) : cg(c,a,b)\)
Search Value (6, 9, 13): \(0.490992067177\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a/\){(b + c)[\(a(b^{2}\) + \(c^{2})\) + \(b^{3}\) + \(c^{3}\)]} (E. Danneels)

▸ Incident Central Lines3 lines

{60, 386}, {261, 1078}, {404, 849}

▸ Functional Relations4 relations