X3630

H⁻¹(X6; M, 1/2)

X3630 = anticomplement of X32455
< 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, 340 }: Central Line L(53, 340) { 1503, 1657 }: Central Line L(1503, 1657) { 548, 3098 }: Central Line L(548, 3098) { 1205, 2854 }: Central Line L(1205, 2854) 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_340 = ISOTOMIC CONJUGATE OF X(265) (1.2317, 1.4188) X_1503 = POINT ARKAB (0.4818, -0.3843) X_1657 = {X(3),X(4)}-HARMONIC CONJUGATE OF X(1656) (0.2755, -0.4853) X_548 = MIDPOINT OF X(5) AND X(20) (0.4719, 0.0286) X_3098 = INTERSECTION OF LINES X(3)X(6) AND X(69)X(74) (0.4500, 0.0195) X_1205 = 3rd SARAGOSSA POINT OF X(67) (0.7329, -0.3693) X_2854 = ISOGONAL CONJUGATE OF X(2770) (0.9944, -0.1682) X_3630 = H-1(X(6); M, 1/2) (0.3184, -0.0354) A B C X2 X6 X53 X340 X1503 X1657 X548 X3098 X1205 X2854 X3630 (a, b, c) = (5, 6, 7) | AB = 1

X3630 (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 \(f(a,b,c) = bc(4a^{2} - 3b^{2} - 3c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.356979833469\)
▸ Incident Central Lines5 lines

{2, 6}, {53, 340}, {548, 3098}, {1205, 2854}, {1503, 1657}

▸ Functional Relations1 relation

  • X3630 = anticomplement of X32455