X2772

ISOGONAL CONJUGATE OF X2688

As the isogonal conjugate of a point on the circumcircle, X2772 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) { 71, 74 }: Central Line L(71, 74) { 102, 110 }: Central Line L(102, 110) { 113, 116 }: Central Line L(113, 116) { 118, 125 }: Central Line L(118, 125) { 146, 150 }: Central Line L(146, 150) { 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_2688 = SR(X(74), X(101)) (0.0051, -0.0224) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_116 = MIDPOINT OF X(4) AND X(103) (0.6990, 0.0375) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_146 = REFLECTION OF X(20) IN X(110) (0.1155, 1.2873) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_2772 = ISOGONAL CONJUGATE OF X(2688) (0.2300, 0.6999) A B C X2688 X71 X74 X102 X110 X113 X116 X118 X125 X146 X150 X30 X511 X2772 (a, b, c) = (5, 6, 7) | AB = 1

X2772 (ISOGONAL CONJUGATE OF X2688) 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 X2688
▸ Alternate Coordinates1 form

  • Trilinears: \(a (a^{5} (b^{2} + c^{2}) - a^{4} (b^{3} + c^{3}) - 2 a^{3} (b^{4} - b^{2} c^{2} + c^{4}) + a^{2} (2 b^{5} - b^{3} c^{2} - b^{2} c^{3} + 2 c^{5}) + a (b^{2} - c^{2})^{2} (b^{2} + c^{2}) - (b - c)^{2} (b^{5} + 2 b^{4} c + 4 b^{3} c^{2} + 4 b^{2} c^{3} + 2 b c^{4} + c^{5})) : :\)

▸ Incident Central Lines8 lines

{30, 511}, {71, 74}, {102, 110}, {113, 116}, {118, 125}, {146, 150}, {1839, 1986}, {2938, 2948}

▸ Functional Relations3 relations