X2911

ORTHIC-ISOGONAL CONJUGATE OF X55

X2911 is the orthic-isogonal conjugate of X55.
< 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 { 41, 71 }: Central Line L(41, 71) { 25, 209 }: Central Line L(25, 209) { 55, 584 }: Central Line L(55, 584) { 56, 583 }: Central Line L(56, 583) { 101, 579 }: Central Line L(101, 579) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_209 = -CEVA CONJUGATE OF X(37) (0.7303, 0.4592) X_584 = ORTHOHARMONIC OF X(500) (0.5720, 0.2209) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_2911 = ORTHIC-ISOGONAL CONJUGATE OF X(55) (0.7645, 0.4625) A B C X55 X1 X6 X41 X71 X25 X209 X584 X56 X583 X101 X579 X2911 (a, b, c) = (5, 6, 7) | AB = 1

X2911 (ORTHIC-ISOGONAL CONJUGATE OF X55) 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) is as described just before X2883
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.935394725966\)
▸ Incident Central Lines18 lines

{1, 6}, {3, 2174}, {25, 209}, {31, 2318}, {41, 71}, {48, 672}, {55, 584}, {56, 583}, {101, 579}, {193, 1332}, {198, 2245}, {393, 1783}, {571, 906}, {607, 1826}, {692, 1974}, {1333, 1801}, {2262, 2348}, {2287, 2345}

▸ Functional Relations7 relations