X3592

ISOGONAL CONJUGATE OF 1st DIXIT POINT

X3592 is the isogonal 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) { 3, 6 }: Brocard Axis { 485, 546 }: Central Line L(485, 546) { 590, 1588 }: Central Line L(590, 1588) { 2, 3591 }: Central Line L(2, 3591) { 487, 3589 }: Central Line L(487, 3589) { 615, 3525 }: Central Line L(615, 3525) 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_485 = VECTEN POINT (0.5773, 0.2578) X_546 = MIDPOINT OF X(4) AND X(5) (0.5842, 0.3223) X_590 = ISOGONAL CONJUGATE OF X(588) (0.5615, 0.2258) X_1588 = POINT CASTOR II (0.5955, 0.2203) X_2 = CENTROID (0.5374, 0.2000) X_3591 = 2nd DIXIT POINT (0.4080, 0.1149) X_487 = ANTICOMPLEMENT OF X(486) (1.7742, 0.6338) X_3589 = ISOGONAL CONJUGATE OF X(3108) (0.5531, 0.2168) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_3525 = EULER LINE INTERCEPT OF LINE X(69)X(575) (0.5306, 0.1822) X_3592 = ISOGONAL CONJUGATE OF 1st DIXIT POINT (0.5737, 0.2238) A B C X3 X6 X485 X546 X590 X1588 X2 X3591 X487 X3589 X615 X3525 X3592 (a, b, c) = (5, 6, 7) | AB = 1

X3592 (ISOGONAL 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 \(f(a,b,c) = a(b^{2} + c^{2} - a^{2} + 6 \operatorname{area}(ABC))\)
Barycentrics: \(a^{2}(2S_{A} + 3S)\) : \(b^{2}(2S_{B} + 3S)\) : \(c^{2}(2S_{C} + 3S)\) [Conway notation]
Search Value (6, 9, 13): \(2.039421186813\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines11 lines

{2, 3591}, {3, 6}, {485, 546}, {487, 3589}, {590, 1588}, {615, 3525}, {1587, 3529}, {2066, 3298}, {2067, 3297}, {3068, 3071}, {3070, 3146}

▸ Functional Relations2 relations