X622

ANTICOMPLEMENT OF X16

X622 is the anticomplement of X16.
< 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, 16 }: Central Line L(2, 16) { 2, 13 }: Central Line L(2, 13) { 4, 69 }: Central Line L(4, 69) { 3, 303 }: Central Line L(3, 303) { 5, 302 }: Central Line L(5, 302) 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_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) 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_303 = ISOTOMIC CONJUGATE OF 2nd NAPOLEON POINT (0.6079, 0.2757) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_302 = ISOTOMIC CONJUGATE OF 1st NAPOLEON POINT (0.5043, 0.1643) X_622 = ANTICOMPLEMENT OF X(16) (-2.0784, -4.0479) A B C Ka Kb Kc X2 X16 X13 X4 X69 X3 X303 X5 X302 X622 (a, b, c) = (5, 6, 7) | AB = 1

X622 (ANTICOMPLEMENT OF X16) 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): \(21.456529369144\)
▸ Alternate Coordinates1 form

  • Trilinears: \(F(16)/a - 2 \sin(A - \pi /3) : F(16)/b - 2 \sin(B - \pi /3) : F(16)/c - 2 \sin(C - \pi /3)\)

▸ Incident Central Lines13 lines

{2, 13}, {3, 303}, {4, 69}, {5, 302}, {14, 532}, {20, 628}, {30, 299}, {183, 1080}, {265, 301}, {298, 381}, {325, 383}, {343, 473}, {394, 472}

▸ Functional Relations7 relations