X2433

ISOGONAL CONJUGATE OF X2407

X2433 is the isogonal conjugate of X2407.
< 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) { 74, 111 }: Central Line L(74, 111) { 2, 525 }: Central Line L(2, 525) { 25, 512 }: Central Line L(25, 512) { 6, 647 }: Central Line L(6, 647) { 526, 686 }: Central Line L(526, 686) { 351, 878 }: Central Line L(351, 878) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_647 = CROSSDIFFERENCE OF X(2) AND X(3) (4.2063, -0.5653) X_686 = CROSSDIFFERENCE OF X(4) AND X(110) (0.1521, -0.4080) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_111 = PARRY POINT (0.9885, -0.0457) X_2 = CENTROID (0.5374, 0.2000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_526 = ISOGONAL CONJUGATE OF X(476) (1.0501, 0.4856) X_351 = CENTER OF THE PARRY CIRCLE (1.3537, 1.1619) X_878 = ISOGONAL CONJUGATE OF X(877) (1.1192, 0.0431) X_2433 = ISOGONAL CONJUGATE OF X(2407) (1.1401, 0.1425) A B C X647 X686 X74 X111 X2 X525 X25 X512 X6 X526 X351 X878 X2433 (a, b, c) = (5, 6, 7) | AB = 1

X2433 (ISOGONAL CONJUGATE OF X2407) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\sin(B - C) \sin A)^{2}/(\csc(C - A) \cos C - \csc(A - B) \cos B) : :\)
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
Search Value (6, 9, 13): \(-3.529683614707\)
▸ Alternate Coordinates2 forms

  • 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: \(a^{2} (b^{2} - c^{2})/(2 a^{4} - b^{4} - c^{4} - a^{2} b^{2} - a^{2} c^{2} + 2 b^{2} c^{2}) : :\)

X2433 lies on the cubic K162.

▸ Incident Central Lines10 lines

{2, 525}, {6, 647}, {25, 512}, {74, 111}, {351, 878}, {468, 879}, {526, 686}, {1637, 1989}, {1648, 2395}, {2420, 2437}

▸ Functional Relations5 relations