xH =(a+b)/(1+ab).
xK= (b-a)/(ab-1), 

donc K est un point fixe.

A = (-1.0063380828590271, 0.006338082859027153)
B = (0.9936619171409729, 0.006338082859027153)
O = Intersect(xAxis, yAxis)
Cr = Circle(O, B)
M = Point(Cr)
a = -0.29999999999999993 (slider from -1 to 1, step 0.1)
b = 0.8 (slider from -1 to 1, step 0.1)
I: (a, 0)
J: (b, 0)
d = Line(M, I)
e = Line(M, J)
C = Intersect(Cr, d, 2)
D = Intersect(Cr, e, 2)
f = Line(C, D)
g = OrthogonalLine(C, f)
K = Intersect(g, xAxis)
h = OrthogonalLine(K, xAxis)
C0, F = Intersect(Cr, h)
i = Line(C0, I)
α = Angle(I, M, J)
G, M0 = Intersect(Cr, i)
j: x = (a + b) / (1 + a b)
β = Angle(D, C, K)
k = Segment(M, O)
l = Segment(O, C)
m = Segment(O, D)
γ = Angle(O, D, C)
δ = Angle(O, C, K)
n = OrthogonalLine(D, f)
L, N = Intersect(Cr, n)
P = Intersect(n, xAxis)
E = Intersect(Cr, g, 2)
p = Segment(D, E)
q = Segment(C, N)
r = Segment(C, E)
s = Segment(D, N)
ε = Angle(N, D, O)
xK: (b - a) / (a b - 1)
c = Line(A, B)
t = Segment(K, C0)
ζ = Angle(C0, K, O)
H: ((a + b) / (1 + a b); 0)
xH: (a + b) / (1 + a b)
η = Angle(I, M0, J)
a_1 = Segment(M0, J)
b_1 = Segment(O, C)
θ = Angle(D, C, E)
B' = (0, 1)
c_1 = OrthogonalLine(O, r)
Q = Intersect(r, c_1)
distanceOQ = Distance(O, Q)
TexteOQ: "\overline{" + (Name[O]) + (Name[Q]) + "} \, = \, " + distanceOQ
o: sin(α)