Solution

The proof here will be very brief, referring to the solution of problem 10.1.24, the value of the invariant for the spiral trajectory was derived.:

$$\frac{Be(d^2-R^2)}{2} = const$$

Where $d$ is the distance from the side circle to the axis of the main orbit, with $d=0$ this equality inevitably follows:

$$BR^2 = const$$