X682

POINT ARNEB

X682 = crosspoint of X3 and X32
< 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, 69 }: Central Line L(3, 69) { 154, 237 }: Central Line L(154, 237) { 248, 695 }: Central Line L(248, 695) 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_32 = 3rd POWER POINT (0.6400, 0.3332) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249) X_682 = POINT ARNEB (0.6397, 0.1604) A B C X3 X32 X69 X154 X237 X248 X695 X682 (a, b, c) = (5, 6, 7) | AB = 1

X682 (POINT ARNEB) 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 \(f(A,B,C) = \sec B \csc^{3} C + \sec C \csc^{3} B\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = \sin A f(A,B,C)\)
Search Value (6, 9, 13): \(214.930646324287\)
▸ Incident Central Lines3 lines

{3, 69}, {154, 237}, {248, 695}

▸ Functional Relations3 relations