X1436

X282-BETH CONJUGATE OF X282

X1436 = isogonal conjugate of X329
< 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) { 3, 9 }: Central Line L(3, 9) { 19, 56 }: Central Line L(19, 56) { 48, 55 }: Central Line L(48, 55) { 189, 333 }: Central Line L(189, 333) { 6, 603 }: Central Line L(6, 603) { 57, 1422 }: Central Line L(57, 1422) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_9 = MITTENPUNKT (0.5110, 0.1615) X_19 = CLAWSON POINT (0.6246, 0.4244) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_189 = CYCLOCEVIAN CONJUGATE OF X(8) (0.6131, 0.7055) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1422 = -BETH CONJUGATE OF X(189) (0.6044, 0.6471) X_1436 = -BETH CONJUGATE OF X(282) (0.6039, 0.6642) A B C X282 X3 X9 X19 X56 X48 X55 X189 X333 X6 X603 X57 X1422 X1436 (a, b, c) = (5, 6, 7) | AB = 1

X1436 (X282-BETH CONJUGATE OF X282) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X282
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.958477929020\)
▸ Incident Central Lines8 lines

{3, 9}, {6, 603}, {19, 56}, {48, 55}, {57, 1422}, {189, 333}, {284, 1433}, {673, 1440}

▸ Functional Relations5 relations