X2779

ISOGONAL CONJUGATE OF X2695

As the isogonal conjugate of a point on the circumcircle, X2779 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) { 35, 73 }: Central Line L(35, 73) { 102, 110 }: Central Line L(102, 110) { 113, 124 }: Central Line L(113, 124) { 117, 125 }: Central Line L(117, 125) { 30, 511 }: Central Line L(30, 511) { 1844, 1845 }: Central Line L(1844, 1845) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2695 = SR(X(74), X(109)) (0.0704, -0.1734) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) 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_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_117 = MIDPOINT OF X(4) AND X(109) (0.4879, 0.4948) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1844 = ZOSMA TRANSFORM OF X(79) (0.6067, 0.3599) X_1845 = ZOSMA TRANSFORM OF X(80) (0.5417, 0.5181) X_2779 = ISOGONAL CONJUGATE OF X(2695) (0.3146, 0.7429) A B C X2695 X35 X73 X102 X110 X113 X124 X117 X125 X30 X511 X1844 X1845 X2779 (a, b, c) = (5, 6, 7) | AB = 1

X2779 (ISOGONAL CONJUGATE OF X2695) 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 X2695
▸ Alternate Coordinates1 form

  • Trilinears: \(a (a^{6} (b^{2} + c^{2}) - a^{5} b c (b + c) - a^{4} (3 b^{4} - b^{3} c - 2 b^{2} c^{2} - b c^{3} + 3 c^{4}) + a^{3} b c (2 b^{3} - b^{2} c - b c^{2} + 2 c^{3}) + a^{2} (b - c)^{2} (3 b^{4} + 4 b^{3} c + 3 b^{2} c^{2} + 4 b c^{3} + 3 c^{4}) - a b c (b - c)^{2} (b^{3} + c^{3}) - (b^{2} - c^{2})^{2} (b^{4} - b^{3} c + 3 b^{2} c^{2} - b c^{3} + c^{4})) : :\)

▸ Incident Central Lines8 lines

{30, 511}, {35, 73}, {102, 110}, {113, 124}, {117, 125}, {1364, 2646}, {1844, 1845}, {2939, 2948}

▸ Functional Relations3 relations