X139

X112-OF-ORTHIC-TRIANGLE

X139 = X112-of-orthic-triangle
< 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) { 52, 129 }: Central Line L(52, 129) { 53, 128 }: Central Line L(53, 128) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_52 = ORTHOCENTER OF ORTHIC TRIANGLE (0.7155, 0.4580) X_129 = -OF-ORTHIC-TRIANGLE (0.4587, 0.4847) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_128 = -OF-ORTHIC-TRIANGLE (0.3310, 0.3690) X_139 = -OF-ORTHIC-TRIANGLE (0.7000, 0.4596) A B C X52 X129 X53 X128 X139 (a, b, c) = (5, 6, 7) | AB = 1

X139 (X112-OF-ORTHIC-TRIANGLE) 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 \(f(A,B,C) = (\sec A)(\sin 2B + \sin 2C)[(\sin 2B - \sin 2C)^{2}][\sin^{2}(2B) + \sin^{2}(2C) - \sin^{2}(2A)] u(A,B,C)\), \(u(A,B,C) = (\sin 2B)^{4} + (\sin 2C)^{4} - (\sin 2A)^{4} + (\sin 2B \sin 2C)[\sin^{2}(2B) + \sin^{2}(2C) - \sin^{2}(2A)]\)
Search Value (6, 9, 13): \(-2.966034811283\)

X139 lies on the nine-point circle.

▸ Incident Central Lines2 lines

{52, 129}, {53, 128}

▸ Functional Relations2 relations

  • X139 = inverse-in-polar-circle of X32692

  • X139 = X112-of-orthic-triangle