X1029

CYCLOCEVIAN CONJUGATE OF X1

X1029 = isogonal conjugate of X1030
< 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) { 10, 191 }: Central Line L(10, 191) { 319, 321 }: Central Line L(319, 321) { 115, 593 }: Central Line L(115, 593) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1030 = ISOGONAL CONJUGATE OF X(1029) (0.5271, 0.1468) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_593 = 1st HATZIPOLAKIS-YIU POINT (0.6202, 0.3026) X_1029 = CYCLOCEVIAN CONJUGATE OF X(1) (0.6026, 0.3320) A B C X1030 X10 X191 X319 X321 X115 X593 X1029 (a, b, c) = (5, 6, 7) | AB = 1

X1029 (CYCLOCEVIAN CONJUGATE OF X1) 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 \(f(a,b,c) = 1/[a + 2(a + b + c) \cos A]\)
Barycentrics: \(1/(a^{3} + a^{2} (b + c) - a (b^{2} + b c + c^{2}) - (b + c) (b^{2} + c^{2})) : :\)
Search Value (6, 9, 13): \(-1.257219679345\)

X1029 lies on the Kiepert hyperbola.

▸ Incident Central Lines3 lines

{10, 191}, {115, 593}, {319, 321}

▸ Functional Relations5 relations