X2424

ISOGONAL CONJUGATE OF X2398

X2424 is the isogonal conjugate of X2398.
< 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) { 103, 106 }: Central Line L(103, 106) { 6, 657 }: Central Line L(6, 657) { 56, 663 }: Central Line L(56, 663) { 269, 513 }: Central Line L(269, 513) { 1, 905 }: Central Line L(1, 905) { 676, 885 }: Central Line L(676, 885) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_677 = TRILINEAR POLE OF LINE X(3)X(101) (1.3200, 0.4790) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_657 = CROSSDIFFERENCE OF X(1) AND X(7) (10.1538, -2.2611) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1 = INCENTER (0.5714, 0.2333) X_905 = POINT ACHERNAR (5.6190, -0.6999) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2449, 0.5665) X_885 = ISOTOMIC CONJUGATE OF X(883) (1.0518, 0.0256) X_2424 = ISOGONAL CONJUGATE OF X(2398) (1.0916, 0.1371) A B C X677 X103 X106 X6 X657 X56 X663 X269 X513 X1 X905 X676 X885 X2424 (a, b, c) = (5, 6, 7) | AB = 1

X2424 (ISOGONAL CONJUGATE OF X2398) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as given just before X2394
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
Search Value (6, 9, 13): \(-2.446427719259\)

X2424 lies on the cubic K162.

▸ Incident Central Lines9 lines

{1, 905}, {6, 657}, {56, 663}, {86, 2400}, {103, 106}, {269, 513}, {665, 911}, {676, 885}, {2283, 2426}

▸ Functional Relations6 relations