X2782

ISOGONAL CONJUGATE OF X2698

As the isogonal conjugate of a point on the circumcircle, X2782 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) { 5, 39 }: Central Line L(5, 39) { 3, 76 }: Central Line L(3, 76) { 4, 147 }: Central Line L(4, 147) { 30, 511 }: Central Line L(30, 511) { 262, 381 }: Central Line L(262, 381) { 140, 620 }: Central Line L(140, 620) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2698 = SR(X(98), X(99)) (0.0271, 0.2938) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_4 = ORTHOCENTER (0.6122, 0.3958) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_620 = MIDPOINT OF X(618) AND X(619) (0.4308, 0.2580) X_2782 = ISOGONAL CONJUGATE OF X(2698) (0.0900, 0.5797) A B C X2698 X5 X39 X3 X76 X4 X147 X30 X511 X262 X381 X140 X620 X2782 (a, b, c) = (5, 6, 7) | AB = 1

X2782 (ISOGONAL CONJUGATE OF X2698) 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 X2698
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines15 lines

{3, 76}, {4, 147}, {5, 39}, {30, 511}, {68, 1987}, {110, 1316}, {140, 620}, {230, 2021}, {262, 381}, {338, 1634}, {385, 2080}, {549, 2482}, {895, 2452}, {1352, 2549}, {2453, 2930}

▸ Functional Relations7 relations