X1662

1st INTERSECTION OF BROCARD AXIS AND 1st LEMOINE CIRCLE

X1662 = reflection of X1663 in X182
< 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) { 1663, 182 }: Brocard Axis { 3, 6 }: Brocard Axis A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1663 = 2nd INTERSECTION OF BROCARD AXIS AND 1st LEMOINE CIRCLE (0.6998, 0.4321) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1662 = 1st INTERSECTION OF BROCARD AXIS AND 1st LEMOINE CIRCLE (0.4002, -0.0628) A B C X1663 X182 X3 X6 X1662 (a, b, c) = (5, 6, 7) | AB = 1

X1662 (1st INTERSECTION OF BROCARD AXIS AND 1st LEMOINE 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 \(f(A,B,C) = e \cos(A - \omega ) + \cos(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(7.608945839696\)
▸ Incident Central Lines3 lines

{3, 6}, {1676, 2040}, {1677, 2039}

▸ Functional Relations3 relations