X535

DIRECTION OF VECTOR AX + BX + CX, where X = X36

< 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) { 2, 36 }: Central Line L(2, 36) { 30, 511 }: Central Line L(30, 511) { 63, 484 }: Central Line L(63, 484) { 226, 551 }: Central Line L(226, 551) { 214, 908 }: Central Line L(214, 908) { 10, 1155 }: Central Line L(10, 1155) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_908 = POINT ACUBENS (-0.8367, -1.7996) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1155 = SCHRÖDER POINT (1.7143, 2.3328) X_535 = DIRECTION OF VECTOR AX + BX + CX, where X = X(36) (0.8224, 0.7130) A B C X2 X36 X30 X511 X63 X484 X226 X551 X214 X908 X10 X1155 X535 (a, b, c) = (5, 6, 7) | AB = 1

X535 (DIRECTION OF VECTOR AX + BX + CX, where X = X36) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (2ax - by - cz)/a\), \(x = x(A,B,C) = 1 - 2 \cos A\), \(y = x(B,C,A)\), \(z = x(C,A,B)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)

X535 lies on the line at infinity.

▸ Incident Central Lines12 lines

{2, 36}, {8, 3245}, {10, 1155}, {30, 511}, {63, 484}, {80, 3218}, {214, 908}, {226, 551}, {376, 2077}, {388, 2078}, {428, 1878}, {903, 1168}