X657

CROSSDIFFERENCE OF X1 AND X7

X657 = crossdifference of every pair of points on line {1, 7}
< 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) { 59, 101 }: Central Line L(59, 101) { 9, 522 }: Central Line L(9, 522) { 44, 513 }: Central Line L(44, 513) { 663, 853 }: Central Line L(663, 853) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_9 = MITTENPUNKT (0.5110, 0.1615) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_853 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(55) (-4.0788, -11.8784) X_657 = CROSSDIFFERENCE OF X(1) AND X(7) (10.1538, -2.2611) A B C X59 X101 X9 X522 X44 X513 X663 X853 X657 (a, b, c) = (5, 6, 7) | AB = 1

X657 (CROSSDIFFERENCE OF X1 AND X7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((1 + \cos A)(\cos B - \cos C) : :\)
Search Value (6, 9, 13): \(-16.329018053623\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(\sec^{2}(B/2) - \sec^{2}(C/2) : :\)

  • Trilinears: \(\tan^{2}(B/2) - \tan^{2}(C/2) : :\)

  • Trilinears: \(a(b - c)(b + c - a)^{2} : :\)

▸ Linear Combinations1 combination

  • X657 = \(2\) X9 + X45755, X649 - \(4\) X22108, \(2\) X4130 - \(3\) X14427, X4171 + \(2\) X4827, X4171 - \(3\) X14427, \(2\) X4827 + \(3\) X14427, \(4\) X14330 - X42462

▸ Incident Central Lines4 lines

{9, 522}, {44, 513}, {59, 101}, {663, 853}

▸ Functional Relations18 relations