X1124

ISOGONAL CONJUGATE OF X1123

X1124 is the isogonal conjugate of X1123.
< 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) { 1, 6 }: Incenter–Symmedian Line { 55, 372 }: Central Line L(55, 372) { 56, 371 }: Central Line L(56, 371) { 11, 485 }: Central Line L(11, 485) { 12, 486 }: Central Line L(12, 486) { 42, 494 }: Central Line L(42, 494) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1123 = PAASCHE POINT (0.5572, 0.2178) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_485 = VECTEN POINT (0.5773, 0.2578) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_494 = 2nd VAN LAMOEN HOMOTHETIC CENTER (0.8529, 0.5391) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) A B C X1123 X1 X6 X55 X372 X56 X371 X11 X485 X12 X486 X42 X494 X1124 (a, b, c) = (5, 6, 7) | AB = 1

X1124 (ISOGONAL CONJUGATE OF X1123) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1 + \sin A : 1 + \sin B : 1 + \sin C\)
Barycentrics: \((1 + \sin A) \sin A : (1 + \sin B) \sin B : (1 + \sin C) \sin C\)
Search Value (6, 9, 13): \(1.405902547496\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a(S + bc) : b(S + ca) : c(S + ab)\)

▸ Incident Central Lines13 lines

{1, 6}, {3, 2066}, {11, 485}, {12, 486}, {35, 1152}, {36, 1151}, {42, 494}, {55, 372}, {56, 371}, {176, 651}, {255, 605}, {498, 615}, {499, 590}

▸ Functional Relations5 relations