X298

ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER

X298 is the isotomic conjugate of 1st 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) { 616, 621 }: Central Line L(616, 621) { 2, 6 }: Centroid–Symmedian Line { 14, 76 }: Central Line L(14, 76) { 13, 532 }: Central Line L(13, 532) { 15, 533 }: Central Line L(15, 533) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_616 = ANTICOMPLEMENT OF X(13) (0.4364, 0.0360) X_621 = ANTICOMPLEMENT OF X(15) (0.5084, 0.2242) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_532 = DIRECTION OF VECTOR AX + BX + CX, where X = X(17) (0.8927, 0.6671) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_533 = DIRECTION OF VECTOR AX + BX + CX, where X = X(18) (0.0625, -0.1448) X_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) A B C X616 X621 X2 X6 X14 X76 X13 X532 X15 X533 X298 (a, b, c) = (5, 6, 7) | AB = 1

X298 (ISOTOMIC CONJUGATE OF 1st 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): \(4.709717205007\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines16 lines

{2, 6}, {3, 617}, {5, 634}, {13, 532}, {14, 76}, {15, 533}, {18, 636}, {99, 531}, {140, 628}, {264, 472}, {316, 530}, {317, 473}, {319, 1082}, {340, 470}, {381, 622}, {511, 1080}

▸ Functional Relations12 relations