X1428

X238-BETH CONJUGATE OF X238

X1428 = X1416-Ceva conjugate of X56
< 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, 41 }: Central Line L(6, 41) { 65, 82 }: Central Line L(65, 82) { 1, 182 }: Central Line L(1, 182) { 36, 511 }: Central Line L(36, 511) { 59, 518 }: Central Line L(59, 518) { 3, 613 }: Central Line L(3, 613) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_1 = INCENTER (0.5714, 0.2333) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_613 = INTERSECTION OF LINES X(1)X(6) AND X(56)X(511) (0.7698, 0.2310) X_1428 = -BETH CONJUGATE OF X(238) (0.5173, 0.1103) A B C X238 X6 X41 X65 X82 X1 X182 X36 X511 X59 X518 X3 X613 X1428 (a, b, c) = (5, 6, 7) | AB = 1

X1428 (X238-BETH CONJUGATE OF X238) 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 \(u : v : w\) = X238
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.150384420532\)
▸ Incident Central Lines18 lines

{1, 182}, {3, 613}, {6, 41}, {31, 1403}, {36, 511}, {57, 985}, {58, 1178}, {59, 518}, {60, 757}, {65, 82}, {184, 614}, {238, 1284}, {499, 1352}, {611, 999}, {651, 1463}, {692, 1279}, {961, 1258}, {1456, 1462}

▸ Functional Relations3 relations