k = 0.58571 (slider from 0 to 1, step 0.01)
A = (-3, 0)
B = Point(xAxis)
G = Rotate(B, 90°, A)
F = Mirror(B, A)
c_E = Circle(F, G)
c_D = Circle(G, A)
E = Point(c_E)
ac = Line(A, E)
c_{EA} = Circle(E, A)
D = Mirror(A, Line[G, E])
bc = Line(B, D)
C = Intersect(ac, bc)
DE = Segment(E, D)
AC = Segment(C, A)
BC = Segment(C, B)
AB = Segment(A, B)
ab = Line(A, B)
by = OrthogonalLine(B, ab)
lieu1 = Locus(C, E)
EE: E
M = Dilate(B, k, A)
asy = Line(M, Line[B, Midpoint[A, G]])