X634

ANTICOMPLEMENT OF X62

X634 is the anticomplement of X62.
< 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, 62 }: Central Line L(2, 62) { 2, 17 }: Central Line L(2, 17) { 4, 69 }: Central Line L(4, 69) { 3, 299 }: Central Line L(3, 299) { 5, 298 }: Central Line L(5, 298) 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_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) 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_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_634 = ANTICOMPLEMENT OF X(62) (0.3230, -0.0820) A B C Ka Kb Kc X2 X62 X17 X4 X69 X3 X299 X5 X298 X634 (a, b, c) = (5, 6, 7) | AB = 1

X634 (ANTICOMPLEMENT OF X62) 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 \(f(a,b,c) = (S_{B}S_{C} - 2 \sqrt{3} S_{A} \operatorname{area})/a\)
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): \(8.637509400092\)
▸ Alternate Coordinates1 form

  • Trilinears: \(F(62)/a + 2 \cos(A + \pi /3) : F(62)/b + 2 \cos(B + \pi /3) : F(62)/c + 2 \cos(C + \pi /3)\)

▸ Incident Central Lines12 lines

{2, 17}, {3, 299}, {4, 69}, {5, 298}, {13, 635}, {18, 624}, {20, 617}, {140, 303}, {141, 397}, {343, 470}, {394, 471}, {398, 524}

▸ Functional Relations4 relations