X2780

ISOGONAL CONJUGATE OF X2696

As the isogonal conjugate of a point on the circumcircle, X2780 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, 111 }: Central Line L(74, 111) { 113, 126 }: Central Line L(113, 126) { 3, 351 }: Central Line L(3, 351) { 30, 511 }: Central Line L(30, 511) { 110, 1296 }: Central Line L(110, 1296) { 895, 2444 }: Central Line L(895, 2444) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2696 = SR(X(74), X(111)) (0.9625, -0.1136) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_111 = PARRY POINT (0.9885, -0.0457) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_126 = -OF-MEDIAL-TRIANGLE (0.3119, 0.3228) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_351 = CENTER OF THE PARRY CIRCLE (1.3537, 1.1619) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_1296 = COLLINGS TRANSFORM OF X(126) (0.0115, 0.2498) X_895 = ISOGONAL CONJUGATE OF X(468) (0.9484, -0.0134) X_2444 = ISOGONAL CONJUGATE OF X(2418) (0.9861, 0.0334) X_2780 = ISOGONAL CONJUGATE OF X(2696) (0.9056, 0.6570) A B C X2696 X74 X111 X113 X126 X3 X351 X30 X511 X110 X1296 X895 X2444 X2780 (a, b, c) = (5, 6, 7) | AB = 1

X2780 (ISOGONAL CONJUGATE OF X2696) 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 X2696
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines6 lines

{3, 351}, {30, 511}, {74, 111}, {110, 1296}, {113, 126}, {895, 2444}

▸ Functional Relations6 relations