X3205

X54-CEVA CONJUGATE OF X61

X3205 = X54-Ceva conjugate of X61
< 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) { 14, 54 }: Central Line L(14, 54) { 49, 61 }: Central Line L(49, 61) { 17, 110 }: Central Line L(17, 110) { 13, 156 }: Central Line L(13, 156) { 62, 184 }: Central Line L(62, 184) { 15, 1147 }: Central Line L(15, 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_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_156 = -OF-TANGENTIAL-TRIANGLE (0.6520, -0.1707) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_1147 = ISOGONAL CONJUGATE OF X(847) (0.8329, 0.3027) X_3205 = -CEVA CONJUGATE OF X(61) (0.5985, 0.2069) A B C X54 X61 X14 X49 X17 X110 X13 X156 X62 X184 X15 X1147 X3205 (a, b, c) = (5, 6, 7) | AB = 1

X3205 (X54-CEVA CONJUGATE OF X61) 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 \(u : v : w\) = X61
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): \(2.769445243571\)
▸ 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, 3200}, {6, 3206}, {13, 156}, {14, 54}, {15, 1147}, {17, 110}, {49, 61}, {62, 184}, {203, 2477}, {3107, 3202}

▸ Functional Relations1 relation