X1043

CEVAPOINT OF X1 AND X20

X1043 is the cevapoint of X1 and X20.
< 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) { 8, 21 }: Central Line L(8, 21) { 29, 33 }: Central Line L(29, 33) { 1, 75 }: Central Line L(1, 75) { 20, 64 }: Central Line L(20, 64) { 99, 103 }: Central Line L(99, 103) { 81, 145 }: Central Line L(81, 145) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_8 = NAGEL POINT (0.4694, 0.1333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_99 = STEINER POINT (0.1109, 0.4322) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_1043 = CEVAPOINT OF X(1) AND X(20) (0.4149, 0.0930) A B C X1 X20 X8 X21 X29 X33 X75 X64 X99 X103 X81 X145 X1043 (a, b, c) = (5, 6, 7) | AB = 1

X1043 (CEVAPOINT OF X1 AND X20) 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 \(f(A,B,C) = 1/[(1 - \cos A)(\cos B + \cos C)]\)
Barycentrics: \((a - b - c)^{2}/(b + c) : :\)
Search Value (6, 9, 13): \(5.347073744796\)
▸ Incident Central Lines15 lines

{1, 75}, {8, 21}, {20, 64}, {27, 306}, {29, 33}, {58, 519}, {72, 190}, {81, 145}, {99, 103}, {200, 341}, {220, 346}, {239, 1104}, {280, 285}, {283, 643}, {286, 322}

▸ Functional Relations9 relations