X2448

1st INTERSECTION(LINE X1X_3, BEVAN CIRCLE)

Of the two points of intersection, X2448 is the closer to X1..
< 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, 3 }: OI Line (Incenter–Circumcenter Line) 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_2448 = 1st INTERSECTION(LINE X(1)X(3), BEVAN CIRCLE) (0.9165, 0.8673) A B C X1 X3 X2448 (a, b, c) = (5, 6, 7) | AB = 1

X2448 (1st INTERSECTION(LINE X1X_3, BEVAN 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 \(f(A,B,C) = D \cos A - (D - 2)(\cos B + \cos C - 1)\), \(D = (3 - 2 \cos A - 2 \cos B - 2 \cos C)^{1/2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-1.931329508291\)

X2448 lies on the Bevan circle.

▸ Incident Central Lines1 line

{1, 3}

▸ Functional Relations3 relations