X583

ORTHOGONAL OF X500

X583 = inverse-in-Brocard-circle of X584
< 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) { 3, 6 }: Brocard Axis { 37, 38 }: Central Line L(37, 38) { 44, 992 }: Central Line L(44, 992) { 71, 1100 }: Central Line L(71, 1100) { 518, 1009 }: Central Line L(518, 1009) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_992 = INTERSECTION OF LINES X(2)X(6) AND X(9)X(39) (0.2678, -0.0897) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1009 = INTERCEPT OF EULER LINE AND LINE X(1)X(39) (0.5532, 0.2412) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) A B C X3 X6 X37 X38 X44 X992 X71 X1100 X518 X1009 X583 (a, b, c) = (5, 6, 7) | AB = 1

X583 (ORTHOGONAL OF X500) 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 \(f(a,b,c) = a(a^{2}b + a^{2}c + 2abc - b^{3} - c^{3})\) (M.Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.396642090479\)
▸ Linear Combinations1 combination

  • X583 = \(s\) X3 + \((r - 3R) \cot(\omega )\) X6

▸ Incident Central Lines5 lines

{3, 6}, {37, 38}, {44, 992}, {71, 1100}, {518, 1009}

▸ Functional Relations1 relation

  • X583 = inverse-in-Brocard-circle of X584