X3593

ISOTOMIC CONJUGATE OF 1st DIXIT POINT

X3593 is the isotomic conjugate of 1st dixit point.
< 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, 6 }: Centroid–Symmedian Line { 4, 1165 }: Central Line L(4, 1165) { 641, 1588 }: Central Line L(641, 1588) { 488, 3091 }: Central Line L(488, 3091) { 76, 3591 }: Central Line L(76, 3591) { 637, 3523 }: Central Line L(637, 3523) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1165 = POINT ALTAIS (0.6433, 0.4613) X_641 = COMPLEMENT OF X(485) (0.5175, 0.1711) X_1588 = POINT CASTOR II (0.5955, 0.2203) X_488 = ANTICOMPLEMENT OF X(485) (0.4576, 0.0844) X_3091 = INTERSECTION OF LINES X(2)X(3) AND X(11)X(153) (0.5673, 0.2783) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_3591 = 2nd DIXIT POINT (0.4080, 0.1149) X_637 = ANTICOMPLEMENT OF X(371) (0.4819, 0.1805) X_3523 = EULER LINE INTERCEPT OF LINE X(35)X(390) (0.5160, 0.1440) X_3593 = ISOTOMIC CONJUGATE OF 1st DIXIT POINT (0.5007, 0.1605) A B C X2 X6 X4 X1165 X641 X1588 X488 X3091 X76 X3591 X637 X3523 X3593 (a, b, c) = (5, 6, 7) | AB = 1

X3593 (ISOTOMIC CONJUGATE OF 1st DIXIT POINT) 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 \(f(a,b,c) = bc(b^{2} + c^{2} - a^{2} + 6 \operatorname{area}(ABC))\)
Barycentrics: \(2S_{A}\) + 3S : \(2S_{B}\) + 3S : \(2S_{C}\) + 3S [Conway notation]
Search Value (6, 9, 13): \(3.944131216960\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (3 + 2 \cot A) \csc A\)

▸ Incident Central Lines6 lines

{2, 6}, {4, 1165}, {76, 3591}, {488, 3091}, {637, 3523}, {641, 1588}

▸ Functional Relations1 relation