X2778

ISOGONAL CONJUGATE OF X2694

As the isogonal conjugate of a point on the circumcircle, X2778 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) { 65, 74 }: Central Line L(65, 74) { 113, 123 }: Central Line L(113, 123) { 30, 511 }: Central Line L(30, 511) { 125, 429 }: Central Line L(125, 429) { 110, 1295 }: Central Line L(110, 1295) { 1717, 1854 }: Central Line L(1717, 1854) 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_2687 = SR(X(74), X(100)) (-0.0092, 0.0687) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_123 = -OF-MEDIAL-TRIANGLE (0.5401, -0.0057) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_429 = EULER X(58)-5th-SUBSTITUTION POINT (0.6024, 0.3700) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_1295 = COLLINGS TRANSFORM OF X(123) (0.4680, -0.4072) X_1717 = MIMOSA TRANSFORM OF X(35) (0.6295, 0.3852) X_1854 = ZOSMA TRANSFORM OF X(208) (0.5955, 0.5353) X_2778 = ISOGONAL CONJUGATE OF X(2694) (0.4078, 0.7723) A B C X4 X2687 X65 X74 X113 X123 X30 X511 X125 X429 X110 X1295 X1717 X1854 X2778 (a, b, c) = (5, 6, 7) | AB = 1

X2778 (ISOGONAL CONJUGATE OF X2694) 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 X2694
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines10 lines

{1, 2935}, {30, 511}, {40, 2915}, {65, 74}, {110, 1295}, {113, 123}, {125, 429}, {1498, 2948}, {1717, 1854}, {1858, 1986}

▸ Functional Relations3 relations