X579

HARMONIC OF X284

X579 = X27-Ceva conjugate of X1
< 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, 7 }: Centroid–Gergonne Line { 3, 6 }: Brocard Axis { 19, 46 }: Central Line L(19, 46) { 1, 71 }: Central Line L(1, 71) { 36, 48 }: Central Line L(36, 48) { 56, 219 }: Central Line L(56, 219) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_19 = CLAWSON POINT (0.6246, 0.4244) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) A B C X27 X1 X2 X7 X3 X6 X19 X46 X71 X36 X48 X56 X219 X579 (a, b, c) = (5, 6, 7) | AB = 1

X579 (HARMONIC OF X284) 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 \(f(a,b,c) = a(a^{2}b + a^{2}c + abc - b^{3} - c^{3})\) (M.Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.263414547670\)
▸ Linear Combinations1 combination

  • X579 = \(s\) X3 - \((r + 2R) \cot(\omega )\) X6

▸ Incident Central Lines14 lines

{1, 71}, {2, 7}, {3, 6}, {19, 46}, {36, 48}, {37, 942}, {40, 387}, {56, 219}, {109, 608}, {165, 380}, {198, 218}, {443, 966}, {474, 965}, {517, 1108}

▸ Functional Relations5 relations