X327

ISOTOMIC CONJUGATE OF X182

X327 is the isotomic conjugate of X182.
< 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) { 5, 76 }: Central Line L(5, 76) { 53, 141 }: Central Line L(53, 141) { 95, 160 }: Central Line L(95, 160) { 4, 276 }: Central Line L(4, 276) { 2, 290 }: Central Line L(2, 290) { 69, 263 }: Central Line L(69, 263) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_4 = ORTHOCENTER (0.6122, 0.3958) X_276 = ISOGONAL CONJUGATE OF X(217) (0.5554, 0.2771) X_2 = CENTROID (0.5374, 0.2000) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6298, 0.3525) X_327 = ISOTOMIC CONJUGATE OF X(182) (0.5260, 0.2156) A B C X182 X5 X76 X53 X141 X95 X160 X4 X276 X2 X290 X69 X263 X327 (a, b, c) = (5, 6, 7) | AB = 1

X327 (ISOTOMIC CONJUGATE OF X182) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\csc^{2} A \sec(A - \omega ) : \csc^{2} B \sec(B - \omega ) : \csc^{2} C \sec(C - \omega )\)
Barycentrics: \(\csc A \sec(A - \omega ) : \csc B \sec(B - \omega ) : \csc C \sec(C - \omega )\)
Search Value (6, 9, 13): \(-9.548082449486\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\sin A \csc(2A - 2 \omega ): \sin B \csc(2B - 2 \omega ) : \sin C \csc(2C - 2 \omega )\)

▸ Incident Central Lines6 lines

{2, 290}, {4, 276}, {5, 76}, {53, 141}, {69, 263}, {95, 160}

▸ Functional Relations4 relations