X2777

ISOGONAL CONJUGATE OF X2693

As the isogonal conjugate of a point on the circumcircle, X2777 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) { 4, 74 }: Central Line L(4, 74) { 3, 113 }: Central Line L(3, 113) { 20, 110 }: Central Line L(20, 110) { 64, 265 }: Central Line L(64, 265) { 30, 511 }: Central Line L(30, 511) { 182, 1177 }: Central Line L(182, 1177) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_477 = TIXIER ANTIPODE (0.0176, -0.0644) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_265 = REFLECTION OF X(3) IN X(125) (0.8606, -0.0500) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_1177 = 1st SARAGOSSA POINT OF X(67) (0.7694, -1.0073) X_2777 = ISOGONAL CONJUGATE OF X(2693) (0.6437, -0.3772) A B C X4 X477 X74 X3 X113 X20 X110 X64 X265 X30 X511 X182 X1177 X2777 (a, b, c) = (5, 6, 7) | AB = 1

X2777 (ISOGONAL CONJUGATE OF X2693) 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 X2693
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines18 lines

{3, 113}, {4, 74}, {5, 1539}, {20, 110}, {23, 1533}, {30, 511}, {64, 265}, {112, 1562}, {182, 1177}, {185, 1986}, {389, 974}, {399, 1498}, {468, 1514}, {550, 1511}, {858, 1531}, {1316, 1561}, {1352, 2892}, {1568, 2071}

▸ Functional Relations2 relations