X624

COMPLEMENT OF X16

X624 is the complement of X16.
< 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) { 623, 625 }: Central Line L(623, 625) { 2, 13 }: Central Line L(2, 13) { 17, 83 }: Central Line L(17, 83) { 5, 141 }: Central Line L(5, 141) { 14, 299 }: Central Line L(14, 299) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_623 = COMPLEMENT OF X(15) (0.5302, 0.2060) X_625 = MIDPOINT OF X(623) AND X(624) (0.2068, -0.3280) X_2 = CENTROID (0.5374, 0.2000) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) 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_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_624 = COMPLEMENT OF X(16) (-0.1165, -0.8620) A B C X623 X625 X2 X13 X17 X83 X5 X141 X14 X299 X624 (a, b, c) = (5, 6, 7) | AB = 1

X624 (COMPLEMENT 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 \(f(a,b,c) = [2(b^{2} + c^{2}) \operatorname{area} - \sqrt{3}(a^{2}S_{A} + 2S_{B}S_{C})]/a\)
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): \(7.336158936653\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines8 lines

{2, 13}, {3, 630}, {5, 141}, {14, 299}, {15, 303}, {17, 83}, {30, 619}, {395, 532}

▸ Functional Relations7 relations