X3631

H⁻¹(X6; M, -2)

X3631 = midpoint of X69 and X141
< 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) { 69, 141 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 320, 594 }: Central Line L(320, 594) { 511, 546 }: Central Line L(511, 546) { 319, 1086 }: Central Line L(319, 1086) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_594 = ISOGONAL CONJUGATE OF X(593) (0.5025, 0.1672) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_546 = MIDPOINT OF X(4) AND X(5) (0.5842, 0.3223) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_3631 = H-1(X(6); M, -2) (0.4592, 0.1159) A B C X69 X141 X2 X6 X320 X594 X511 X546 X319 X1086 X3631 (a, b, c) = (5, 6, 7) | AB = 1

X3631 (H⁻¹(X6; M, -2)) 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 \(f(a,b,c) = bc(2a^{2} - 3b^{2} - 3c^{2})\)
Barycentrics: \(2a^{2} - 3b^{2} - 3c^{2} : 2b^{2} - 3c^{2} - 3a^{2} : 2c^{2} - 3a^{2} - 3b^{2}\)
Search Value (6, 9, 13): \(4.674944164268\)
▸ Incident Central Lines10 lines

{2, 6}, {319, 1086}, {320, 594}, {338, 1232}, {382, 1352}, {511, 546}, {545, 2321}, {550, 1503}, {1350, 3529}, {3530, 3564}

▸ Functional Relations1 relation