X738

ISOGONAL CONJUGATE OF X728

X738 is the isogonal conjugate of X728.
< 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) { 56, 269 }: Central Line L(56, 269) { 57, 279 }: Central Line L(57, 279) { 9, 348 }: Central Line L(9, 348) { 77, 951 }: Central Line L(77, 951) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_728 = INTERSECTION OF LINES X(8)X(9) AND X(57)X(345) (0.3648, 0.0624) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_9 = MITTENPUNKT (0.5110, 0.1615) X_348 = ISOTOMIC CONJUGATE OF X(281) (0.4854, 0.1069) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_951 = ISOGONAL CONJUGATE OF X(950) (0.5800, 0.2727) X_738 = ISOGONAL CONJUGATE OF X(728) (0.6449, 0.4466) A B C X728 X56 X269 X57 X279 X9 X348 X77 X951 X738 (a, b, c) = (5, 6, 7) | AB = 1

X738 (ISOGONAL CONJUGATE OF X728) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c - a) ^{-3}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.007065173776\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\tan^{3}(A/2) : \tan^{3}(B/2) : \tan^{3}(C/2)\) (M. Iliev, 4/12/07)

▸ Incident Central Lines4 lines

{9, 348}, {56, 269}, {57, 279}, {77, 951}

▸ Functional Relations3 relations