X2854

ISOGONAL CONJUGATE OF X2770

X2854 is the isogonal conjugate of X2770.
< 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) { 6, 110 }: Central Line L(6, 110) { 67, 69 }: Central Line L(67, 69) { 125, 126 }: Central Line L(125, 126) { 30, 511 }: Central Line L(30, 511) { 373, 597 }: Central Line L(373, 597) { 159, 1177 }: Central Line L(159, 1177) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2770 = SR(X(110), X(111)) (0.0375, 0.3178) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_67 = ISOGONAL CONJUGATE OF X(23) (0.7606, -0.2152) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_126 = -OF-MEDIAL-TRIANGLE (0.3119, 0.3228) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID (0.5614, 0.2395) X_597 = MIDPOINT OF X(2) AND X(6) (0.5687, 0.2336) X_159 = -OF-TANGENTIAL-TRIANGLE (0.4211, -0.7266) X_1177 = 1st SARAGOSSA POINT OF X(67) (0.7694, -1.0073) X_2854 = ISOGONAL CONJUGATE OF X(2770) (0.9944, -0.1682) A B C X2770 X6 X110 X67 X69 X125 X126 X30 X511 X373 X597 X159 X1177 X2854 (a, b, c) = (5, 6, 7) | AB = 1

X2854 (ISOGONAL CONJUGATE OF X2770) 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 X2770
Barycentrics: \(a^{2}(b^{6} + c^{6} - a^{4}b^{2} - a^{4}c^{2} + 4a^{2}b^{2}c^{2} - 2b^{4}c^{2} - 2b^{2}c^{4}) : :\)
▸ Incident Central Lines11 lines

{6, 110}, {30, 511}, {67, 69}, {74, 1296}, {125, 126}, {159, 1177}, {182, 1511}, {265, 1352}, {373, 597}, {399, 1351}, {1112, 1843}

▸ Functional Relations4 relations