 \vec{ MA }. \vec{ MB } \; = \; k²  

A = (-0.89470828302262, 0.36314819414890304)
B = (0.5428471348697522, 0.33312092693444095)
a = Segment(A, B)
O = Midpoint(a)
k = 0.37 (slider from 0 to 2, step 0.01)
c = Circle(O, sqrt(a * a / 4.0 + k * k))
M = Point(c)
b = Segment(A, M)
d = Segment(M, B)
e = Segment(M, O)