Two circles geometry problems
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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$(-d\cos\theta, -d\sin\theta)$.
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.
as shown in the figure. I am not a mathematician. So, take me easy! Thank in advance !
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Matthew Mishrikey
2022-1-4
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
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