X241

X1-LINE CONJUGATE OF X55

X241 = X1-Hirst inverse of X57
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 7, 37 }: Central Line L(7, 37) { 6, 77 }: Central Line L(6, 77) { 2, 85 }: Central Line L(2, 85) { 63, 220 }: Central Line L(63, 220) { 218, 222 }: Central Line L(218, 222) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_7 = GERGONNE POINT (0.5903, 0.2769) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_2 = CENTROID (0.5374, 0.2000) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) A B C X1 X55 X3 X7 X37 X6 X77 X2 X85 X63 X220 X218 X222 X241 (a, b, c) = (5, 6, 7) | AB = 1

X241 (X1-LINE CONJUGATE OF X55) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos^{4} B/2 - [\cos^{2}(A/2)][\cos^{2}(B/2) +\cos^{2}(C/2)] + \cos^{4}(C/2) : :\)
Barycentrics: \((b^{2} + c^{2})(1 - \cos A) - a^{2}(\cos B + \cos C) : :\)
Search Value (6, 9, 13): \(-0.807702666211\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines15 lines

{1, 3}, {2, 85}, {6, 77}, {7, 37}, {9, 269}, {44, 651}, {63, 220}, {141, 307}, {218, 222}, {239, 664}, {277, 278}, {294, 910}, {347, 1108}, {514, 650}, {960, 1042}

▸ Functional Relations15 relations