X3498

INTERSECTION OF LINES X3X_83 AND X194X_263

< 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) { 3, 83 }: Central Line L(3, 83) { 3495, 3501 }: Central Line L(3495, 3501) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_3495 = INTERSECTION OF LINES X(32)X(983) AND X(39)X(256) (0.4713, 0.1344) X_3501 = INTERSECTION OF LINES X(1)X(39) AND X(4)X(9) (0.5467, 0.2440) X_3498 = INTERSECTION OF LINES X(3)X(83) AND X(194)X(263) (0.6232, 0.3554) A B C X3 X83 X3495 X3501 X3498 (a, b, c) = (5, 6, 7) | AB = 1

X3498 (INTERSECTION OF LINES X3X_83 AND X194X_263) 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 \(f(a,b,c) = bc[2a^{6}(b^{2} + c^{2}) + a^{4}(b^{4} + 3b^{2}c^{2} + c^{4}) + a^{2}b^{2}c^{2}(b^{2} + c^{2}) + b^{4}c^{4}]/(a^{4} - a^{2}b^{2} - a^{2}c^{2} - 2b^{2}c^{2}) (E\). Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.186240445827\)

X3498 lies on the cubic Z(X384).

▸ Incident Central Lines2 lines

{3, 83}, {3495, 3501}