X3478

ISOGONAL CONJUGATE OF X3476

X3478 is the isogonal conjugate of X3476.
< 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) { 3, 902 }: Central Line L(3, 902) { 77, 1122 }: Central Line L(77, 1122) { 1, 1828 }: Central Line L(1, 1828) { 1037, 1457 }: Central Line L(1037, 1457) { 219, 2347 }: Central Line L(219, 2347) { 1473, 1795 }: Central Line L(1473, 1795) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3476 = INTERSECTION OF LINES X(1)X(4) AND X(8)X(56) (0.5835, 0.2814) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_1122 = 1st GRINBERG POINT (0.6289, 0.3227) X_1 = INCENTER (0.5714, 0.2333) X_1828 = ZOSMA TRANSFORM OF X(8) (0.6327, 0.4332) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_1457 = -BETH CONJUGATE OF X(517) (0.7719, 1.0314) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_2347 = -ISOCONJUGATE OF X(1476) (0.5740, 0.2042) X_1473 = -BETH CONJUGATE OF X(1040) (0.5906, 0.1432) X_1795 = INVERSE MIMOSA TRANSFORM OF X(36) (0.7464, -0.0703) X_3478 = ISOGONAL CONJUGATE OF X(3476) (0.5577, 0.1884) A B C X3476 X3 X902 X77 X1122 X1 X1828 X1037 X1457 X219 X2347 X1473 X1795 X3478 (a, b, c) = (5, 6, 7) | AB = 1

X3478 (ISOGONAL CONJUGATE OF X3476) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = 1/(2 - \cos A - \cos B - \cos C + \cos B \cos C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.373590335054\)
▸ Incident Central Lines6 lines

{1, 1828}, {3, 902}, {77, 1122}, {219, 2347}, {1037, 1457}, {1473, 1795}

▸ Functional Relations1 relation