X728

INTERSECTION OF LINES X8X_9 AND X57X_345

X728 = X346-Ceva conjugate of X200
< 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) { 8, 9 }: Central Line L(8, 9) { 57, 345 }: Central Line L(57, 345) { 200, 220 }: Central Line L(200, 220) { 78, 644 }: Central Line L(78, 644) { 40, 1018 }: Central Line L(40, 1018) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_738 = ISOGONAL CONJUGATE OF X(728) (0.6449, 0.4466) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_644 = TRILINEAR MULTIPLIER FOR YFF PARABOLA (-0.0171, 0.3359) X_40 = BEVAN POINT (0.4286, -0.0292) X_1018 = -CROSS CONJUGATE OF X(1) (0.1051, 0.4358) X_728 = INTERSECTION OF LINES X(8)X(9) AND X(57)X(345) (0.3648, 0.0624) A B C X738 X8 X9 X57 X345 X200 X220 X78 X644 X40 X1018 X728 (a, b, c) = (5, 6, 7) | AB = 1

X728 (INTERSECTION OF LINES X8X_9 AND X57X_345) 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 \(f(a,b,c) = (b + c - a)^{3}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(5.755881898237\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cot^{3}(A/2) : \cot^{3}(B/2) : \cot^{3}(C/2)\) (M. Iliev, 4/12/07)

▸ Incident Central Lines5 lines

{8, 9}, {40, 1018}, {57, 345}, {78, 644}, {200, 220}

▸ Functional Relations4 relations