X2458

INVERSE-IN-1st-LEMOINE CIRCLE OF X39

X2458 = midpoint of X2461 and X2462
< 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) { 2461, 2462 }: 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_2461 = INVERSE-IN-1st-LEMOINE-CIRCLE OF X(371) (2.0301, 2.6291) X_2462 = INVERSE-IN-1st-LEMOINE-CIRCLE OF X(372) (0.6863, 0.4097) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2458 = INVERSE-IN-1st-LEMOINE CIRCLE OF X(39) (1.3582, 1.5194) A B C X2461 X2462 X3 X6 X2458 (a, b, c) = (5, 6, 7) | AB = 1

X2458 (INVERSE-IN-1st-LEMOINE CIRCLE OF X39) 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 \(f(A,B,C) = \sin A - \sin 3\omega \cos(A - \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-2.073285099598\)
▸ Incident Central Lines1 line

{3, 6}

▸ Functional Relations3 relations