X1418

X142-BETH CONJUGATE OF X142

X1418 = crosspoint of X57 and X279
< 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) { 7, 37 }: Central Line L(7, 37) { 6, 57 }: Central Line L(6, 57) { 77, 1100 }: Central Line L(77, 1100) { 56, 1279 }: Central Line L(56, 1279) { 142, 1212 }: Central Line L(142, 1212) { 553, 1214 }: Central Line L(553, 1214) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_7 = GERGONNE POINT (0.5903, 0.2769) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_1279 = MIDPOINT OF X(1) AND X(238) (1.0952, 0.8554) X_1212 = ISOGONAL CONJUGATE OF X(1170) (0.5256, 0.1789) X_553 = POINT MAIA II (0.5963, 0.2857) X_1214 = ISOGONAL CONJUGATE OF X(1172) (0.5087, 0.1180) X_1418 = -BETH CONJUGATE OF X(142) (0.6200, 0.3311) A B C X142 X7 X37 X6 X57 X77 X1100 X56 X1279 X1212 X553 X1214 X1418 (a, b, c) = (5, 6, 7) | AB = 1

X1418 (X142-BETH CONJUGATE OF X142) 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 \(u : v : w\) = X142
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.251877433326\)
▸ Incident Central Lines16 lines

{6, 57}, {7, 37}, {44, 1445}, {56, 1279}, {65, 1458}, {77, 1100}, {142, 1212}, {354, 2293}, {553, 1214}, {603, 1456}, {942, 991}, {1014, 1333}, {1086, 1108}, {1104, 1448}, {1122, 1400}, {1155, 1253}

▸ Functional Relations4 relations