X1642

TRIPOLAR CENTROID OF X100

X1642 is the tripolar centroid of X100.
< 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) { 1, 6 }: Incenter–Symmedian Line { 241, 1025 }: Central Line L(241, 1025) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_1025 = INTERSECTION OF LINES X(2)X(7) AND X(100)X(109) (1.0996, 1.0180) X_1642 = TRIPOLAR CENTROID OF X(100) (1.0821, 0.8398) A B C X1 X6 X241 X1025 X1642 (a, b, c) = (5, 6, 7) | AB = 1

X1642 (TRIPOLAR CENTROID OF X100) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((a b + a c - b^{2} - c^{2}) (2 a^{3} - 2 a^{2} (b + c) + a (b^{2} + c^{2}) - (b - c)^{2} (b + c)) : :\)
Search Value (6, 9, 13): \(0.023795192692\)
▸ Incident Central Lines2 lines

{1, 6}, {241, 1025}