X2774

ISOGONAL CONJUGATE OF X2690

As the isogonal conjugate of a point on the circumcircle, X2774 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, 103 }: Central Line L(74, 103) { 101, 110 }: Central Line L(101, 110) { 113, 118 }: Central Line L(113, 118) { 116, 125 }: Central Line L(116, 125) { 146, 152 }: Central Line L(146, 152) { 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_2690 = SR(X(74), X(103)) (0.9949, 0.2266) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_146 = REFLECTION OF X(20) IN X(110) (0.1155, 1.2873) X_152 = REFLECTION OF X(20) IN X(101) (0.0408, 1.2414) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_2774 = ISOGONAL CONJUGATE OF X(2690) (0.0375, -0.1074) A B C X2690 X74 X103 X101 X110 X113 X118 X116 X125 X146 X152 X30 X511 X2774 (a, b, c) = (5, 6, 7) | AB = 1

X2774 (ISOGONAL CONJUGATE OF X2690) 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 X2690
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines7 lines

{30, 511}, {74, 103}, {101, 110}, {113, 118}, {116, 125}, {146, 152}, {1282, 2948}

▸ Functional Relations4 relations