X3551

ISOGONAL CONJUGATE OF X3550

X3551 is the isogonal conjugate of X3550.
< 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) { 8, 726 }: Central Line L(8, 726) { 1, 1463 }: Central Line L(1, 1463) { 9, 1575 }: Central Line L(9, 1575) { 983, 1423 }: Central Line L(983, 1423) { 87, 3123 }: Central Line L(87, 3123) { 1149, 2320 }: Central Line L(1149, 2320) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_1 = INCENTER (0.5714, 0.2333) X_8 = NAGEL POINT (0.4694, 0.1333) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_1463 = -BETH CONJUGATE OF X(726) (1.0830, 0.8620) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1575 = EXSIMILICENTER OF SPIEKER AND (1/2)-MOSES CIRCLES (2.5675, 1.8684) X_983 = ISOGONAL CONJUGATE OF X(982) (0.5890, 0.2731) X_1423 = -BETH CONJUGATE OF X(192) (0.6537, 0.3692) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_3123 = DANNEELS PERSPECTOR FOR X(43) (0.8179, 0.1482) X_1149 = ISOGONAL CONJUGATE OF X(1120) (1.1667, 0.8165) X_2320 = -ISOCONJUGATE OF X(1405) (0.5446, 0.1940) X_3551 = ISOGONAL CONJUGATE OF X(3550) (0.5173, 0.1667) A B C X982 X1 X8 X726 X1463 X9 X1575 X983 X1423 X87 X3123 X1149 X2320 X3551 (a, b, c) = (5, 6, 7) | AB = 1

X3551 (ISOGONAL CONJUGATE OF X3550) 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 \(f(a,b,c) = 1/(2a^{2} + bc - ca - ab)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.752272446966\)

X3551 lies on the Feuerbach hyperbola.

▸ Incident Central Lines6 lines

{1, 1463}, {8, 726}, {9, 1575}, {87, 3123}, {983, 1423}, {1149, 2320}

▸ Functional Relations2 relations