X2773

ISOGONAL CONJUGATE OF X2689

As the isogonal conjugate of a point on the circumcircle, X2773 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) { 74, 102 }: Central Line L(74, 102) { 109, 110 }: Central Line L(109, 110) { 113, 117 }: Central Line L(113, 117) { 124, 125 }: Central Line L(124, 125) { 146, 151 }: Central Line L(146, 151) { 30, 511 }: Central Line L(30, 511) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2689 = SR(X(74), X(102)) (0.9296, 0.3775) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_117 = MIDPOINT OF X(4) AND X(109) (0.4879, 0.4948) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_146 = REFLECTION OF X(20) IN X(110) (0.1155, 1.2873) X_151 = REFLECTION OF X(20) IN X(109) (0.3395, 1.3793) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_2773 = ISOGONAL CONJUGATE OF X(2689) (1.0803, 0.4228) A B C X2689 X74 X102 X109 X110 X113 X117 X124 X125 X146 X151 X30 X511 X2773 (a, b, c) = (5, 6, 7) | AB = 1

X2773 (ISOGONAL CONJUGATE OF X2689) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as at X2689
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines6 lines

{30, 511}, {74, 102}, {109, 110}, {113, 117}, {124, 125}, {146, 151}

▸ Functional Relations3 relations