X3471

ISOGONAL CONJUGATE OF X3470

X3471 is the isogonal conjugate of X3470.
< 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) { 140, 523 }: Central Line L(140, 523) { 477, 550 }: Central Line L(477, 550) { 5, 1117 }: Central Line L(5, 1117) { 3, 1138 }: Central Line L(3, 1138) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1511 = FERMAT CROSSSUM (0.3758, 0.3250) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_477 = TIXIER ANTIPODE (0.0176, -0.0644) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1117 = POINT ALRESCHA (0.9978, 0.0022) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1138 = ISOGONAL CONJUGATE OF X(399) (-0.2714, 0.2752) X_3471 = ISOGONAL CONJUGATE OF X(3470) (1.0333, -0.0176) A B C X1511 X30 X140 X523 X477 X550 X5 X1117 X3 X1138 X3471 (a, b, c) = (5, 6, 7) | AB = 1

X3471 (ISOGONAL CONJUGATE OF X3470) 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 \(f(a,b,c) = 1/x(3471)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-35.176632701802\)

X3471 lies on the Napoleon cubic.

▸ Incident Central Lines4 lines

{3, 1138}, {5, 1117}, {140, 523}, {477, 550}

▸ Functional Relations2 relations