X240

X1-LINE CONJUGATE OF X48

X240 = X1-Hirst inverse of X19
< 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) { 1, 19 }: Central Line L(1, 19) { 38, 92 }: Central Line L(38, 92) { 75, 158 }: Central Line L(75, 158) { 4, 256 }: Central Line L(4, 256) { 162, 896 }: Central Line L(162, 896) { 63, 1096 }: Central Line L(63, 1096) 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_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_19 = CLAWSON POINT (0.6246, 0.4244) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_4 = ORTHOCENTER (0.6122, 0.3958) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (2.0357, 2.1579) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1096 = TRILINEAR SQUARE OF X(19) (0.6263, 0.5385) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) A B C X1 X48 X19 X38 X92 X75 X158 X4 X256 X162 X896 X63 X1096 X240 (a, b, c) = (5, 6, 7) | AB = 1

X240 (X1-LINE CONJUGATE OF X48) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec A \cos(A + \omega ) : \sec B \cos(B + \omega ) : \sec C \cos(C + \omega )\)
Barycentrics: \(\tan A \cos(A + \omega ) : \tan B \cos(B + \omega ) : \tan C \cos(C + \omega )\)
Search Value (6, 9, 13): \(1.236230318224\)
▸ Alternate Coordinates1 form

  • Trilinears: \((a^{2} b^{2} + a^{2} c^{2} - b^{4} - c^{4})/(a^{2} - b^{2} - c^{2}) : :\)

▸ Incident Central Lines11 lines

{1, 19}, {4, 256}, {38, 92}, {63, 1096}, {75, 158}, {162, 896}, {278, 982}, {281, 984}, {522, 656}, {607, 611}, {608, 613}

▸ Functional Relations12 relations