X299

ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER

X299 is the isotomic conjugate of 2nd isogonic center.
< 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) { 617, 622 }: Central Line L(617, 622) { 2, 6 }: Centroid–Symmedian Line { 13, 76 }: Central Line L(13, 76) { 14, 533 }: Central Line L(14, 533) { 16, 532 }: Central Line L(16, 532) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_617 = ANTICOMPLEMENT OF X(14) (-0.2146, 0.8285) X_622 = ANTICOMPLEMENT OF X(16) (-2.0784, -4.0479) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_533 = DIRECTION OF VECTOR AX + BX + CX, where X = X(18) (0.0625, -0.1448) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_532 = DIRECTION OF VECTOR AX + BX + CX, where X = X(17) (0.8927, 0.6671) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) A B C X617 X622 X2 X6 X13 X76 X14 X533 X16 X532 X299 (a, b, c) = (5, 6, 7) | AB = 1

X299 (ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\csc^{2} A \sin(A - \pi /3) : \csc^{2} B \sin(B - \pi /3) : \csc^{2} C \sin(C - \pi /3)\)
Barycentrics: \(\csc A \sin(A - \pi /3) : \csc B \sin(B - \pi /3) : \csc C \sin(C - \pi /3)\)
Search Value (6, 9, 13): \(10.298886101292\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(S - \sqrt{3} S_{A} : :\)

▸ Incident Central Lines18 lines

{2, 6}, {3, 616}, {5, 633}, {13, 76}, {14, 533}, {16, 532}, {17, 635}, {30, 617}, {75, 554}, {99, 530}, {140, 627}, {264, 473}, {316, 531}, {317, 472}, {319, 559}, {340, 471}, {381, 621}, {383, 511}

▸ Functional Relations12 relations