a \sqrt{ 3 } 

2a

E = (-9.887932695914548, 0.7285634914038998)
F = (43.079848093802575, 1.1530603988905017)
c = Line(E, F)
A = (0.25282676070983384, -2.7145780915429834)
B = (8.931430202658142, -2.6674117684889165)
a = Segment(A, B)
b = OrthogonalLine(B, a)
d = Circle(A, a * 2.0)
C = Intersect(d, b, 2.0)
e = Segment(C, A)
f = Segment(C, B)
α = Angle(B, A, C)
β = Angle(C, B, A)