X319

ISOTOMIC CONJUGATE OF X79

X319 is the isotomic conjugate of X79.
< 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) { 894, 594 }: Central Line L(894, 594) { 7, 8 }: Gergonne–Nagel Line { 10, 86 }: Central Line L(10, 86) { 141, 239 }: Central Line L(141, 239) { 80, 313 }: Central Line L(80, 313) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_594 = ISOGONAL CONJUGATE OF X(593) (0.5025, 0.1672) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) A B C X894 X594 X7 X8 X10 X86 X141 X239 X80 X313 X319 (a, b, c) = (5, 6, 7) | AB = 1

X319 (ISOTOMIC CONJUGATE OF X79) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((1 + 2 \cos A)/a^{2} : :\)
Barycentrics: \(( 1 + 2 \cos A)/a : :\)
Search Value (6, 9, 13): \(4.880305067180\)
▸ Alternate Coordinates2 forms

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

  • Barycentrics: \(b c + 2 S_{A} : :\)

▸ Incident Central Lines16 lines

{2, 1100}, {7, 8}, {10, 86}, {80, 313}, {141, 239}, {171, 757}, {200, 326}, {261, 502}, {298, 1082}, {299, 559}, {306, 333}, {307, 664}, {317, 318}, {321, 1029}, {344, 391}, {524, 594}

▸ Functional Relations5 relations