X3474

INTERSECTION OF LINES X4X_46 AND X7X_55

X3474 = cevapoint of X46 and X1721
< 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) { 4, 46 }: Central Line L(4, 46) { 7, 55 }: Central Line L(7, 55) { 20, 65 }: Central Line L(20, 65) { 144, 210 }: Central Line L(144, 210) { 1, 376 }: Central Line L(1, 376) { 109, 278 }: Central Line L(109, 278) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_1721 = MIMOSA TRANSFORM OF X(55) (0.6494, 0.4136) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_1 = INCENTER (0.5714, 0.2333) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_3474 = INTERSECTION OF LINES X(4)X(46) AND X(7)X(55) (0.6682, 0.4369) A B C X46 X1721 X4 X7 X55 X20 X65 X144 X210 X1 X376 X109 X278 X3474 (a, b, c) = (5, 6, 7) | AB = 1

X3474 (INTERSECTION OF LINES X4X_46 AND X7X_55) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(- \cos A + \cos B + \cos C + \cos B \cos C : :\)
Barycentrics: \(3 a^{3} - a^{2} (b + c) - a (b - c)^{2} - (b - c)^{2} (b + c) : :\)
Search Value (6, 9, 13): \(-1.876912771487\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines34 lines

{1, 376}, {2, 1155}, {4, 46}, {7, 55}, {8, 529}, {20, 65}, {25, 1633}, {33, 1721}, {40, 388}, {42, 3000}, {43, 2635}, {56, 962}, {57, 497}, {63, 2550}, {73, 1044}, {79, 498}, {109, 278}, {144, 210}, {165, 226}, {196, 243}, {200, 527}, {212, 948}, {329, 1376}, {354, 390}, {412, 1118}, {484, 1478}, {515, 2093}, {528, 2094}, {580, 1777}, {653, 1857}, {658, 2898}, {1040, 2263}, {1707, 1738}, {1761, 2345}

▸ Functional Relations4 relations