X3629

H⁻¹(X6; M, 1/2)

< 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) { 2, 6 }: Centroid–Symmedian Line { 53, 648 }: Central Line L(53, 648) { 397, 621 }: Central Line L(397, 621) { 398, 622 }: Central Line L(398, 622) { 511, 550 }: Central Line L(511, 550) { 546, 576 }: Central Line L(546, 576) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_397 = CROSSPOINT OF X(4) AND X(17) (0.6029, 0.2975) X_621 = ANTICOMPLEMENT OF X(15) (0.5084, 0.2242) X_398 = CROSSPOINT OF X(4) AND X(18) (0.5945, 0.2099) X_622 = ANTICOMPLEMENT OF X(16) (-2.0784, -4.0479) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_546 = MIDPOINT OF X(4) AND X(5) (0.5842, 0.3223) X_576 = ORTHOHARMONIC OF X(187) (0.6500, 0.3498) X_3629 = H-1(X(6); M, 1/2) (0.6939, 0.3681) A B C X2 X6 X53 X648 X397 X621 X398 X622 X511 X550 X546 X576 X3629 (a, b, c) = (5, 6, 7) | AB = 1

X3629 (H⁻¹(X6; M, 1/2)) 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 \(f(a,b,c) = bc(4a^{2} - b^{2} - c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.461781951069\)
▸ Incident Central Lines15 lines

{2, 6}, {53, 648}, {182, 3530}, {317, 1990}, {382, 1351}, {397, 621}, {398, 622}, {487, 3594}, {488, 3592}, {511, 550}, {518, 3244}, {542, 1539}, {546, 576}, {1112, 1843}, {1350, 3528}