X584

ORTHOHARMONIC OF X500

X584 = inverse-in-Brocard-circle of X583
< 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, 41 }: Central Line L(37, 41) { 48, 354 }: Central Line L(48, 354) { 42, 560 }: Central Line L(42, 560) 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_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_354 = WEILL POINT (0.5823, 0.2533) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_560 = 4th POWER POINT (0.6520, 0.3639) X_584 = ORTHOHARMONIC OF X(500) (0.5720, 0.2209) A B C X3 X6 X37 X41 X48 X354 X42 X560 X584 (a, b, c) = (5, 6, 7) | AB = 1

X584 (ORTHOHARMONIC 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 \(f(a,b,c) = a(ab^{2} + ac^{2} + bc^{2} + b^{2}c + 2abc - a^{3})\) (M.Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.931776158859\)
▸ Linear Combinations1 combination

  • X584 = \(s\) X3 + \((r + 3R) \cot(\omega )\) X6

▸ Incident Central Lines4 lines

{3, 6}, {37, 41}, {42, 560}, {48, 354}

▸ Functional Relations1 relation

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