X2781

ISOGONAL CONJUGATE OF X2697

As the isogonal conjugate of a point on the circumcircle, X2781 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, 67 }: Central Line L(4, 67) { 6, 74 }: Central Line L(6, 74) { 22, 110 }: Central Line L(22, 110) { 51, 125 }: Central Line L(51, 125) { 69, 146 }: Central Line L(69, 146) { 113, 127 }: Central Line L(113, 127) 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_842 = ISOGONAL CONJUGATE OF X(542) (-0.0101, 0.1156) X_67 = ISOGONAL CONJUGATE OF X(23) (0.7606, -0.2152) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_22 = EXETER POINT (0.4143, -0.1221) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_146 = REFLECTION OF X(20) IN X(110) (0.1155, 1.2873) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_127 = -OF-MEDIAL-TRIANGLE (0.5480, -0.0061) X_2781 = ISOGONAL CONJUGATE OF X(2697) (0.3989, 0.7702) A B C X4 X842 X67 X6 X74 X22 X110 X51 X125 X69 X146 X113 X127 X2781 (a, b, c) = (5, 6, 7) | AB = 1

X2781 (ISOGONAL CONJUGATE OF X2697) 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 X2697
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines14 lines

{3, 1177}, {4, 67}, {6, 74}, {22, 110}, {30, 511}, {51, 125}, {64, 895}, {66, 265}, {69, 146}, {113, 127}, {159, 399}, {185, 1205}, {206, 1511}, {1498, 2930}

▸ Functional Relations3 relations