X340

ISOTOMIC CONJUGATE OF X265

X340 is the isotomic conjugate of X265.
< 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) { 648, 297 }: Central Line L(648, 297) { 4, 69 }: Central Line L(4, 69) { 95, 140 }: Central Line L(95, 140) { 67, 290 }: Central Line L(67, 290) { 250, 325 }: Central Line L(250, 325) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_67 = ISOGONAL CONJUGATE OF X(23) (0.7606, -0.2152) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_250 = ISOGONAL CONJUGATE OF X(125) (0.5892, 0.5347) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_340 = ISOTOMIC CONJUGATE OF X(265) (1.2317, 1.4188) A B C X648 X297 X4 X69 X95 X140 X67 X290 X250 X325 X340 (a, b, c) = (5, 6, 7) | AB = 1

X340 (ISOTOMIC CONJUGATE OF X265) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec A \sin 3A \csc^{3} A : :\)
Barycentrics: \(\sec A \sin 3A \csc^{2} A : :\)
Search Value (6, 9, 13): \(5.166990648448\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines10 lines

{4, 69}, {67, 290}, {95, 140}, {250, 325}, {297, 524}, {298, 470}, {299, 471}, {447, 540}, {458, 599}, {520, 850}

▸ Functional Relations7 relations