X3206

X54-CEVA CONJUGATE OF X62

X3206 = X54-Ceva conjugate of X62
< 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) { 13, 54 }: Central Line L(13, 54) { 49, 62 }: Central Line L(49, 62) { 18, 110 }: Central Line L(18, 110) { 14, 156 }: Central Line L(14, 156) { 61, 184 }: Central Line L(61, 184) { 16, 1147 }: Central Line L(16, 1147) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_54 = KOSNITA POINT (0.5880, 0.2176) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_156 = -OF-TANGENTIAL-TRIANGLE (0.6520, -0.1707) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_1147 = ISOGONAL CONJUGATE OF X(847) (0.8329, 0.3027) X_3206 = -CEVA CONJUGATE OF X(62) (0.5890, -0.1843) A B C X54 X62 X13 X49 X18 X110 X14 X156 X61 X184 X16 X1147 X3206 (a, b, c) = (5, 6, 7) | AB = 1

X3206 (X54-CEVA CONJUGATE OF X62) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X54 and \(u : v : w\) = X62
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(0.395725755695\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(\sin(A - \pi /6) \sin(2A + \pi /6) : \sin(B - \pi /6) \sin(2B + \pi /6) : \sin(C - \pi /6) \sin(2C + \pi /6)\) (M. Iliev, 4/12/07)

  • Trilinears: \(\cos 3A - \cos(A + \pi /3) : \cos 3B - \cos(B + \pi /3) : \cos 3C - \cos(C + \pi /3)\) (M. Iliev, 4/12/07)

▸ Incident Central Lines10 lines

{3, 3201}, {6, 3205}, {13, 54}, {14, 156}, {16, 1147}, {18, 110}, {49, 62}, {61, 184}, {202, 2477}, {3106, 3202}

▸ Functional Relations1 relation