X349

ISOTOMIC CONJUGATE OF X284

X349 is the isotomic conjugate of X284.
< 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) { 76, 85 }: Central Line L(76, 85) { 75, 225 }: Central Line L(75, 225) { 12, 313 }: Central Line L(12, 313) { 73, 290 }: Central Line L(73, 290) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_290 = ISOGONAL CONJUGATE OF X(237) (0.7829, -0.1380) X_349 = ISOTOMIC CONJUGATE OF X(284) (0.5089, 0.1906) A B C X226 X307 X76 X85 X75 X225 X12 X313 X73 X290 X349 (a, b, c) = (5, 6, 7) | AB = 1

X349 (ISOTOMIC CONJUGATE OF X284) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\cos B + \cos C)\csc^{3} A : (\cos C + \cos A)\csc^{3} B : (\cos A + \cos B) \csc^{3} C\)
Barycentrics: \((\cos B + \cos C)\csc^{2} A : (\cos C + \cos A)\csc^{2} B : (\cos A + \cos B)(\csc C/2)^{2}\)
Search Value (6, 9, 13): \(2.841479126417\)
▸ Alternate Coordinates1 form

  • Trilinears: \((\cos B + \cos C)\csc(A - \omega ) : (\cos C + \cos A)\csc(B - \omega ) : (\cos A + \cos B)\csc(C - \omega )\)

▸ Incident Central Lines4 lines

{12, 313}, {73, 290}, {75, 225}, {76, 85}

▸ Functional Relations4 relations