attraction

\hat{ANB}<\hat{AMB}

\hat{ANB}>\hat{AMB}

\hat{ANB}=\hat{AMB}

\hat{ANB}= 2 \hat{AMB}

a = 0.33 (slider from 0 to 3, step 0.01)
NN = (5.396, 2.366)
M = (0.776, 3.598)
C = (3.46, -1.374)
nc = Segment(NN, C)
c = Circle(C, M)
BB = Point(c)
A = Point(c)
A' = Mirror(A, C)
b = Segment(BB, A')
B = DynamicCoordinates(BB, If[b < a, x(A'), x(BB)], If[b < a, y(A'), y(BB)])
NP = ClosestPoint(c, NN)
n = Segment(NN, NP)
N = DynamicCoordinates(NN, If[n < a, x(NP), If[nc < a, x(C), x(NN)]], If[n < a, y(NP), If[nc < a, y(C), y(NN)]])
a_1 = Ray(M, A)
d = Ray(N, A)
e = Ray(N, B)
b_1 = Ray(M, B)
α = Angle(A, M, B)
β = Angle(A, N, B)
f = CircleArc(C, A, B)
texte1: "2    \hat{AMB}=2×" + (LaTeX[α]) + "=" + (LaTeX[2 * α]) + ""
m = Segment(C, M)
g = Segment(A, B)