X938

ANTICOMPLEMENT OF X936

X938 is the anticomplement of X936.
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 936 }: Nagel Line { 1, 2 }: Nagel Line { 4, 7 }: Central Line L(4, 7) { 20, 57 }: Central Line L(20, 57) { 29, 81 }: Central Line L(29, 81) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_936 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(9) (0.5138, 0.1768) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_938 = ANTICOMPLEMENT OF X(936) (0.5846, 0.2462) A B C Ka Kb Kc X2 X936 X1 X4 X7 X20 X57 X29 X81 X938 (a, b, c) = (5, 6, 7) | AB = 1

X938 (ANTICOMPLEMENT OF X936) 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 \(f(a,b,c) = bc[a^{4} - 2a^{3}(b + c) - 4a^{2}bc + (b - c)(b^{2} - c^{2})(2a - b - c)]\)
Search Value (6, 9, 13): \(1.520086101657\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cos A' : :\), where A' is the angle formed by the tangents from the A-excenter to the incircle

▸ Incident Central Lines13 lines

{1, 2}, {4, 7}, {20, 57}, {29, 81}, {40, 390}, {56, 411}, {63, 452}, {65, 497}, {354, 388}, {355, 1056}, {517, 1058}, {774, 986}, {944, 999}

▸ Functional Relations3 relations