X3016

(LEMOINE AXIS)∩(FERMAT AXIS)

X3016 = reflection of X2088 in X2493
< 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) { 2088, 2493 }: Central Line L(2088, 2493) { 6, 13 }: Central Line L(6, 13) { 187, 237 }: Central Line L(187, 237) { 316, 323 }: Central Line L(316, 323) { 543, 2421 }: Central Line L(543, 2421) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2088 = PK-TRANSFORM OF X(110) (0.2299, -0.3440) X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE} (-0.6894, 1.3058) 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_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_323 = ISOTOMIC CONJUGATE OF X(94) (-0.8839, -1.3275) X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X(99) (0.0220, 0.4806) X_2421 = ISOGONAL CONJUGATE OF X(2395) (1.5174, 1.2531) X_3016 = (LEMOINE AXIS)∩(FERMAT AXIS) (-1.6086, 2.9556) A B C X2088 X2493 X6 X13 X187 X237 X316 X323 X543 X2421 X3016 (a, b, c) = (5, 6, 7) | AB = 1

X3016 ((LEMOINE 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 \(f(A,B,C) = \csc B \sin(A - B)[1 + 2 \cos(2C)] + \csc C \sin(A - C)[1 + 2 \cos(2B)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-1.260295621624\)
▸ Incident Central Lines6 lines

{6, 13}, {187, 237}, {316, 323}, {543, 2421}, {1843, 2971}, {2088, 2493}

▸ Functional Relations2 relations