X3200

X54-CEVA CONJUGATE OF X15

X3200 = X54-Ceva conjugate of X15
< 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) { 18, 54 }: Central Line L(18, 54) { 49, 62 }: Central Line L(49, 62) { 13, 110 }: Central Line L(13, 110) { 16, 184 }: Central Line L(16, 184) { 202, 215 }: Central Line L(202, 215) { 61, 1147 }: Central Line L(61, 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_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) 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_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_202 = -CEVA CONJUGATE OF X(15) (0.5962, 0.2697) X_215 = -CEVA CONJUGATE OF X(50) (0.4113, 0.3887) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_1147 = ISOGONAL CONJUGATE OF X(847) (0.8329, 0.3027) X_3200 = -CEVA CONJUGATE OF X(15) (0.6345, 0.2451) A B C X54 X15 X18 X49 X62 X13 X110 X16 X184 X202 X215 X61 X1147 X3200 (a, b, c) = (5, 6, 7) | AB = 1

X3200 (X54-CEVA CONJUGATE OF X15) 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 \(u : v : w\) = X15
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): \(-9.906000554911\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(\sin(A + \pi /3) \sin(2A + 2\pi /3) : \sin(B + \pi /3) \sin(2B + 2\pi /3) : \sin(C + \pi /3) \sin(2C + 2\pi /3)\) (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 Lines9 lines

{3, 3205}, {6, 3201}, {13, 110}, {16, 184}, {18, 54}, {49, 62}, {61, 1147}, {202, 215}, {3105, 3202}

▸ Functional Relations3 relations