X623

COMPLEMENT OF X15

X623 is the complement of X15.
< 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) { 624, 625 }: Central Line L(624, 625) { 2, 14 }: Central Line L(2, 14) { 18, 83 }: Central Line L(18, 83) { 5, 141 }: Central Line L(5, 141) { 13, 298 }: Central Line L(13, 298) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_624 = COMPLEMENT OF X(16) (-0.1165, -0.8620) X_625 = MIDPOINT OF X(623) AND X(624) (0.2068, -0.3280) X_2 = CENTROID (0.5374, 0.2000) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_623 = COMPLEMENT OF X(15) (0.5302, 0.2060) A B C X624 X625 X2 X14 X18 X83 X5 X141 X13 X298 X623 (a, b, c) = (5, 6, 7) | AB = 1

X623 (COMPLEMENT 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 \(f(a,b,c) = [2(b^{2} + c^{2}) \operatorname{area} + \sqrt{3} (S_{A}a^{2} + 2S_{B}S_{C})]/a\)
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): \(2.392831178406\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines9 lines

{2, 14}, {3, 629}, {5, 141}, {13, 298}, {16, 302}, {17, 633}, {18, 83}, {30, 618}, {396, 533}

▸ Functional Relations7 relations