Coordonnées de M' :  

x=α-sinα

y=1-cosα

Courbe “compagnon” :

y=1-cosx

A = Point(yAxis)
c = Circle(A, 1)
M = Intersect(c, xAxis, 1)
α = 4.3 (slider from 0 to (2 * π))
A': (α, 1)
M': (α - sin(α), 1 - cos(α))
lieu1 = Locus(M', α)
u = Vector((0, 1), (α, 1))
d = Circle(A', 1)
f = OrthogonalLine(M', xAxis)
H = Intersect(xAxis, f)
g = Segment(M', H)
h = Segment(M', A')
i = OrthogonalLine(A', g)
J = Intersect(g, i)
j = Segment(J, A')
t1, a', m', j_1 = Polygon(M', J, A')
β = Angle(M', A', H)
k = Segment(A', H)
p: y = 1 - cos(x)
l = OrthogonalLine(M', yAxis)
B, C = Intersect(c, l)
D = Intersect(yAxis, l)
E = Intersect(p, l, (-4.299999997454619, 1.4007991744119668))
m = Segment(C, D)
n = Segment(M', E)
U: (π, 0)
q = OrthogonalLine(U, xAxis)
V = Intersect(p, q, (3.141592653589793, 2))
F, W = Intersect(c, yAxis)
r = Segment(W, V)
G = Intersect(p, l, (-4.299999997454619, 1.4007991744119668))
s = Segment(M', G)
I = Intersect(p, l, (1.9831853097249674, 1.4007991744119666))
t = Segment(M', I)
K = Intersect(l, m)
L = Intersect(l, m)
N = Intersect(p, l, (1.9831853097249674, 1.4007991744119666))