Two circles geometry problems

Circle1 with radius intersects with Circle 2 with radius . The Circle 1 has center , and Circle 2 has the center at the initial point. When the Circle 1 rotates with an angle θ, the Circle 2 that is attached to the Circle 1 change its coordination of the centre from to$(-d\cos\theta, -d\sin\theta)$.

I have a problem determining as shown in the figure.

I am not a mathematician. So, take me easy! Thank in advance !

Answer 1

[Matthew Mishrikey]

Not clear from the second drawing what the dl of interest is.

Let's assume dl is the distance between the left edge of each circle.

Then

d_l = -r_1 - (-d cos \theta - r_2)

Therefore

d_l / d_\theta = d sin \theta