X2771

ISOGONAL CONJUGATE OF X2687

As the isogonal conjugate of a point on the circumcircle, X2771 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) { 11, 113 }: Central Line L(11, 113) { 21, 104 }: Central Line L(21, 104) { 65, 79 }: Central Line L(65, 79) { 72, 74 }: Central Line L(72, 74) { 3, 191 }: Central Line L(3, 191) { 119, 125 }: Central Line L(119, 125) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2694 = SR(X(74), X(108)) (0.1842, -0.2988) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_2771 = ISOGONAL CONJUGATE OF X(2687) (0.8887, -0.2701) A B C X2694 X3 X11 X113 X21 X104 X65 X79 X72 X74 X191 X119 X125 X2771 (a, b, c) = (5, 6, 7) | AB = 1

X2771 (ISOGONAL CONJUGATE OF X2687) 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 X2687
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines18 lines

{1, 399}, {3, 191}, {11, 113}, {21, 104}, {30, 511}, {36, 1749}, {65, 79}, {72, 74}, {78, 2932}, {109, 1807}, {119, 125}, {146, 149}, {153, 355}, {214, 960}, {500, 2292}, {946, 1484}, {1464, 1725}, {1829, 1986}

▸ Functional Relations6 relations

Notes

Let Ia be the reflection of X1 in the perpendicular bisector of BC, and define Ib and Ic cyclically. Then X2771 = X30-of-IaIbIc; IaIbIc is the inner Garcia triangle. (Randy Hutson, February 10, 2016)

Let AeBeCe and AiBiCi be the Ae and Ai triangles (aka K798e and K798i triangles). Let Ae’ be the Ai-isogonal conjugate of Ae, and define Be’ and Ce’ cyclically. Let Ai’ be the Ae-isogonal conjugate of Ai, and define Bi’ and Ci’ cyclically. Triangles Ae’Be’Ce’ and Ai’Bi’Ci’ are inversely congruent, with similitude center X2771. Triangle Ai’Bi’Ci’ is also the cross-triangle of the Ae and Ai triangles. (Randy Hutson, June 7, 2019)