X3018

(ORTHIC AXIS)∩(FERMAT AXIS)

X3018 = crosspoint of X2 and X477
< 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, 13 }: Central Line L(6, 13) { 230, 231 }: Central Line L(230, 231) { 112, 393 }: Central Line L(112, 393) { 111, 1302 }: Central Line L(111, 1302) { 1249, 2165 }: Central Line L(1249, 2165) { 1609, 2079 }: Central Line L(1609, 2079) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_477 = TIXIER ANTIPODE (0.0176, -0.0644) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_111 = PARRY POINT (0.9885, -0.0457) X_1302 = COLLINGS TRANSFORM OF X(381) (0.3827, 0.5987) X_1249 = ISOGONAL CONJUGATE OF X(1073) (-0.9482, -15.9845) X_2165 = -ISOCONJUGATE OF X(47) (-0.1110, -0.0295) X_1609 = TCC-PERSPECTOR OF X(19) (0.7601, 0.5316) X_2079 = INVERSE-IN-CIRCUMCIRCLE OF X(115) (1.5334, 0.0268) X_3018 = (ORTHIC AXIS)∩(FERMAT AXIS) (-0.0536, 1.0628) A B C X2 X477 X6 X13 X230 X231 X112 X393 X111 X1302 X1249 X2165 X1609 X2079 X3018 (a, b, c) = (5, 6, 7) | AB = 1

X3018 ((ORTHIC AXIS)∩(FERMAT AXIS)) 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 \(f(A,B,C) = \cos B \sin(A - B)[1 + 2 \cos(2C)] + \cos C \sin(A - C)[1 + 2 \cos(2B)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.625644185396\)
▸ Incident Central Lines6 lines

{6, 13}, {111, 1302}, {112, 393}, {230, 231}, {1249, 2165}, {1609, 2079}

▸ Functional Relations4 relations