X2508

RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, MOSES CIRCLE}

< 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) { 115, 804 }: Central Line L(115, 804) { 512, 2032 }: Central Line L(512, 2032) { 525, 2485 }: Central Line L(525, 2485) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_804 = ODD (- 2, 2) INFINITY POINT (0.9171, 0.6474) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_2032 = RADICAL TRACE OF MOSES AND 1st LEMOINE CIRCLES (0.7198, 0.4650) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_2485 = RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT CIRCLE} (2.1894, 0.2056) X_2508 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, MOSES CIRCLE} (0.9539, 0.3233) A B C X115 X804 X512 X2032 X525 X2485 X2508 (a, b, c) = (5, 6, 7) | AB = 1

X2508 (RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, MOSES CIRCLE}) 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 \(f(a,b,c) = a(b^{2} - c^{2})[a^{8} - b^{8} - c^{8} + b^{2}c^{2}(b^{4} + c^{4} - a^{4})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.897541229272\)
▸ Incident Central Lines3 lines

{115, 804}, {512, 2032}, {525, 2485}