X1419

X144-BETH CONJUGATE OF X144

X1419 = X1-Ceva conjugate 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) { 6, 57 }: Central Line L(6, 57) { 9, 77 }: Central Line L(9, 77) { 41, 738 }: Central Line L(41, 738) { 347, 527 }: Central Line L(347, 527) { 1, 971 }: Central Line L(1, 971) { 73, 991 }: Central Line L(73, 991) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_9 = MITTENPUNKT (0.5110, 0.1615) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_738 = ISOGONAL CONJUGATE OF X(728) (0.6449, 0.4466) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = X(7) (0.8698, 0.6836) X_1 = INCENTER (0.5714, 0.2333) X_971 = INTERSECTION OF LINES X(3)X(9) AND X(4)X(7) (0.6441, 0.7770) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_991 = INTERSECTION OF LINES X(1)X(7) AND X(3)X(6) (0.5514, 0.1870) X_1419 = -BETH CONJUGATE OF X(144) (0.5457, 0.0944) A B C X144 X6 X57 X9 X77 X41 X738 X347 X527 X1 X971 X73 X991 X1419 (a, b, c) = (5, 6, 7) | AB = 1

X1419 (X144-BETH CONJUGATE OF X144) 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 \(u : v : w\) = X144
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.008889274929\)
▸ Incident Central Lines11 lines

{1, 971}, {6, 57}, {7, 1449}, {9, 77}, {41, 738}, {48, 1461}, {73, 991}, {109, 1253}, {347, 527}, {1201, 1420}, {1443, 1445}

▸ Functional Relations4 relations