X621

ANTICOMPLEMENT OF X15

X621 is the anticomplement of X15.
< 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, 15 }: Central Line L(2, 15) { 2, 14 }: Central Line L(2, 14) { 4, 69 }: Central Line L(4, 69) { 3, 302 }: Central Line L(3, 302) { 5, 303 }: Central Line L(5, 303) 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_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_302 = ISOTOMIC CONJUGATE OF 1st NAPOLEON POINT (0.5043, 0.1643) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_303 = ISOTOMIC CONJUGATE OF 2nd NAPOLEON POINT (0.6079, 0.2757) X_621 = ANTICOMPLEMENT OF X(15) (0.5084, 0.2242) A B C Ka Kb Kc X2 X15 X14 X4 X69 X3 X302 X5 X303 X621 (a, b, c) = (5, 6, 7) | AB = 1

X621 (ANTICOMPLEMENT OF X15) 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 \(f(a,b,c) = [\sqrt{3} S_{B}S_{C} + 2S_{A} \operatorname{area}]/a\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.683218336157\)
▸ Alternate Coordinates1 form

  • Trilinears: \(F(15)/a - 2 \sin(A + \pi /3) : F(15)/b - 2 \sin(B + \pi /3) : F(15)/c - 2 \sin(C + \pi /3)\)

▸ Incident Central Lines13 lines

{2, 14}, {3, 302}, {4, 69}, {5, 303}, {13, 533}, {20, 627}, {30, 298}, {183, 383}, {265, 300}, {299, 381}, {325, 1080}, {343, 472}, {394, 473}

▸ Functional Relations7 relations