X635

COMPLEMENT OF X61

X635 is the complement of X61.
< 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) { 61, 633 }: Central Line L(61, 633) { 2, 18 }: Central Line L(2, 18) { 5, 141 }: Central Line L(5, 141) { 17, 299 }: Central Line L(17, 299) { 62, 298 }: Central Line L(62, 298) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_633 = ANTICOMPLEMENT OF X(61) (0.4457, 0.1049) X_2 = CENTROID (0.5374, 0.2000) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_635 = COMPLEMENT OF X(61) (0.5179, 0.1858) A B C X61 X633 X2 X18 X5 X141 X17 X299 X62 X298 X635 (a, b, c) = (5, 6, 7) | AB = 1

X635 (COMPLEMENT OF X61) 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 \(f(a,b,c) = [2S_{B}S_{C} + S_{A}a^{2} + 2 \sqrt{3} (b^{2} + c^{2}) \operatorname{area}]/a\)
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): \(2.983199048303\)
▸ Alternate Coordinates1 form

  • Trilinears: \(F(61)/a - \cos(A - \pi /3) : F(61)/b - \cos(B - \pi /3) : F(61)/c - \cos(C - \pi /3)\)

▸ Incident Central Lines9 lines

{2, 18}, {3, 618}, {5, 141}, {13, 634}, {16, 627}, {17, 299}, {62, 298}, {140, 619}, {397, 532}

▸ Functional Relations3 relations