X891

ISOTOMIC CONJUGATE OF X889

As the isogonal conjugate of a point on the circumcircle, X891 lies on the line at infinity.
< 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) { 30, 511 }: Central Line L(30, 511) { 1, 659 }: Central Line L(1, 659) { 244, 665 }: Central Line L(244, 665) { 291, 876 }: Central Line L(291, 876) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_889 = INTERSECTION OF LINES X(99)X(898) AND X(190)X(649) (0.8340, -0.1151) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1 = INCENTER (0.5714, 0.2333) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.9286, 2.2162) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_665 = CROSSDIFFERENCE OF X(2) AND X(11) (1.4579, 1.0988) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_876 = ISOTOMIC CONJUGATE OF X(874) (0.9873, -0.0185) X_891 = ISOTOMIC CONJUGATE OF X(889) (0.8689, 0.6842) A B C X889 X30 X511 X1 X659 X244 X665 X291 X876 X891 (a, b, c) = (5, 6, 7) | AB = 1

X891 (ISOTOMIC CONJUGATE OF X889) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(bv - cw)/(a^{2}u^{2} - bcvw) : :\), where \(u : v : w\) = X513
▸ Alternate Coordinates1 form

  • Trilinears: \((b - c) (a b + a c - 2 b c) : :\)

▸ Incident Central Lines4 lines

{1, 659}, {30, 511}, {244, 665}, {291, 876}

▸ Functional Relations9 relations