X3013

(ANTIORTHIC AXIS)∩(FERMAT AXIS)

X3013 = X477-Ceva conjugate of X55
< 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) { 44, 513 }: Central Line L(44, 513) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_477 = TIXIER ANTIPODE (0.0176, -0.0644) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) 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_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_3013 = (ANTIORTHIC AXIS)∩(FERMAT AXIS) (-3.3712, 5.1010) A B C X477 X55 X6 X13 X44 X513 X3013 (a, b, c) = (5, 6, 7) | AB = 1

X3013 ((ANTIORTHIC 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 \(f(A,B,C) = \sin(A - B)[1 + 2 \cos(2C)] + \sin(A - C)[1 + 2 \cos(2B)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-3.582656638819\)
▸ Incident Central Lines2 lines

{6, 13}, {44, 513}

▸ Functional Relations2 relations