X1401

X38-BETH CONJUGATE OF X38

X1401 = crosspoint of X7 and 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) { 43, 57 }: Central Line L(43, 57) { 56, 58 }: Central Line L(56, 58) { 51, 244 }: Central Line L(51, 244) { 7, 310 }: Central Line L(7, 310) { 65, 519 }: Central Line L(65, 519) { 354, 1122 }: Central Line L(354, 1122) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_7 = GERGONNE POINT (0.5903, 0.2769) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_354 = WEILL POINT (0.5823, 0.2533) X_1122 = 1st GRINBERG POINT (0.6289, 0.3227) X_1401 = -BETH CONJUGATE OF X(38) (0.6188, 0.3077) A B C X38 X43 X57 X56 X58 X51 X244 X7 X310 X65 X519 X354 X1122 X1401 (a, b, c) = (5, 6, 7) | AB = 1

X1401 (X38-BETH CONJUGATE OF X38) 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 \(u : v : w\) = X38
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.366411481673\)
▸ Incident Central Lines13 lines

{7, 310}, {43, 57}, {51, 244}, {56, 58}, {65, 519}, {226, 1463}, {354, 1122}, {511, 982}, {1106, 1425}, {1355, 1365}, {1356, 1366}, {1402, 1458}, {1407, 1460}

▸ Functional Relations3 relations