X1416

X105-BETH CONJUGATE OF X105

X1416 = cevapoint of X56 and X1428
< 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) { 31, 57 }: Central Line L(31, 57) { 32, 56 }: Central Line L(32, 56) { 6, 1362 }: Central Line L(6, 1362) { 58, 1414 }: Central Line L(58, 1414) { 727, 927 }: Central Line L(727, 927) { 738, 1106 }: Central Line L(738, 1106) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1362 = BRISSE TRANSFORM OF X(105) (0.4408, 0.4266) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_1414 = -BETH CONJUGATE OF X(99) (0.3368, 0.5766) X_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT (1.0060, 0.1685) X_927 = ISOGONAL CONJUGATE OF X(926) (1.0037, 0.1836) X_738 = ISOGONAL CONJUGATE OF X(728) (0.6449, 0.4466) X_1106 = TRILINEAR SQUARE OF X(56) (0.6507, 0.4375) X_1416 = -BETH CONJUGATE OF X(105) (1.0588, -0.1921) A B C X105 X31 X57 X32 X56 X6 X1362 X58 X1414 X727 X927 X738 X1106 X1416 (a, b, c) = (5, 6, 7) | AB = 1

X1416 (X105-BETH CONJUGATE OF X105) 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 \(u : v : w\) = X105
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.182086321162\)
▸ Incident Central Lines11 lines

{6, 1362}, {31, 57}, {32, 56}, {58, 1414}, {294, 1468}, {727, 927}, {738, 1106}, {919, 1458}, {951, 1193}, {1357, 1397}, {1395, 1435}

▸ Functional Relations4 relations