X208

X4-CEVA CONJUGATE OF X34

X208 = isogonal conjugate of X271
< 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) { 4, 57 }: Central Line L(4, 57) { 33, 64 }: Central Line L(33, 64) { 1, 102 }: Central Line L(1, 102) { 40, 196 }: Central Line L(40, 196) { 19, 225 }: Central Line L(19, 225) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_1 = INCENTER (0.5714, 0.2333) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_40 = BEVAN POINT (0.4286, -0.0292) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) X_19 = CLAWSON POINT (0.6246, 0.4244) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) A B C X4 X34 X25 X57 X33 X64 X1 X102 X40 X196 X19 X225 X208 (a, b, c) = (5, 6, 7) | AB = 1

X208 (X4-CEVA CONJUGATE OF X34) 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 \(f(A,B,C) = (1 - \sec A)(\cos B + \cos C - \cos A - 1)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.136997167121\)
▸ Incident Central Lines9 lines

{1, 102}, {4, 57}, {19, 225}, {25, 34}, {33, 64}, {40, 196}, {198, 227}, {226, 406}, {318, 653}

▸ Functional Relations5 relations