X339

ISOTOMIC CONJUGATE OF X250

X339 is the isotomic conjugate of X250.
< 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) { 3, 76 }: Central Line L(3, 76) { 115, 127 }: Central Line L(115, 127) { 69, 265 }: Central Line L(69, 265) { 264, 381 }: Central Line L(264, 381) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_250 = ISOGONAL CONJUGATE OF X(125) (0.5892, 0.5347) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_127 = -OF-MEDIAL-TRIANGLE (0.5480, -0.0061) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_265 = REFLECTION OF X(3) IN X(125) (0.8606, -0.0500) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_339 = ISOTOMIC CONJUGATE OF X(250) (0.6002, 0.0170) A B C X250 X3 X76 X115 X127 X69 X265 X264 X381 X339 (a, b, c) = (5, 6, 7) | AB = 1

X339 (ISOTOMIC CONJUGATE OF X250) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((b^{2} - c^{2})^{2}(\cos A)/a^{4} : (c^{2} - a^{2})^{2}(\cos B)/b^{4} : (a^{2} - b^{2})^{2}(\cos C)/c^{4}\)
Barycentrics: \((b^{2} - c^{2})^{2}(\cos A)/a^{3} : (c^{2} - a^{2})^{2}(\cos B)/b^{3} : (a^{2} - b^{2})^{2}(\cos C)/c^{3}\)
Search Value (6, 9, 13): \(5.009222601597\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(\csc A \cot A \sin^{2}(B - C) : \csc B \cot B \sin^{2}(C - A) : \csc C \cot C \sin^{2}(A - B)\)

  • Barycentrics: \(\cot A \sin^{2}(B - C) : \cot B \sin^{2}(C - A) : \cot C \sin^{2}(A - B)\)

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

X339 lies on the MacBeath inconic.

▸ Incident Central Lines4 lines

{3, 76}, {69, 265}, {115, 127}, {264, 381}

▸ Functional Relations5 relations