 \vec{ MA }. \vec{ MB } \; = \; MO² \; - \; d²  

R = 0.6 (slider from 0 to 2, step 0.1)
O = (-0.09523229343756723, 0.4081890949705962)
c = Circle(O, R)
M = (-1.2212548139798955, 0.05912211360247444)
C_1 = (0.9181879750505282, 0.10416301442416757)
a = Line(M, C_1)
A = Intersect(c, a, 1.0)
B = Intersect(c, a, 2.0)
d = Segment(M, O)
e = Semicircle(O, M)
T = Intersect(c, e, 1.0)
b = Segment(M, T)
f = Segment(O, T)
α = Angle(O, T, M)