X1427

X226-BETH CONJUGATE OF X226

X1427 = cevapoint of X1042 and X1400
< 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) { 25, 34 }: Central Line L(25, 34) { 6, 57 }: Central Line L(6, 57) { 2, 85 }: Central Line L(2, 85) { 42, 65 }: Central Line L(42, 65) { 37, 226 }: Central Line L(37, 226) { 278, 393 }: Central Line L(278, 393) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_2 = CENTROID (0.5374, 0.2000) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_1427 = -BETH CONJUGATE OF X(226) (0.6319, 0.3688) A B C X226 X25 X34 X6 X57 X2 X85 X42 X65 X37 X278 X393 X1427 (a, b, c) = (5, 6, 7) | AB = 1

X1427 (X226-BETH CONJUGATE OF X226) 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 \(u : v : w\) = X226
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.079789210056\)
▸ Incident Central Lines20 lines

{2, 85}, {3, 1448}, {6, 57}, {7, 941}, {25, 34}, {31, 1456}, {37, 226}, {42, 65}, {77, 940}, {111, 934}, {212, 1155}, {278, 393}, {307, 1211}, {354, 1458}, {581, 942}, {1014, 1169}, {1106, 1451}, {1333, 1396}, {1406, 1454}, {1412, 1461}

▸ Functional Relations7 relations