Rotate this so that it becomes tangent to another

[marlon]

Notice the space where the pointer is. There should not be a space.

 

Forget the smallest circle in the drawing. My only concern is the two 'donut' figures. I need to rotate them using the upper-right donut as base point.

 

I need to rotate them so that the lower-left donut becomes exactly tangent with the arc.

 

How do I find the tangent point of the lower-left donut and the arc when I rotate the donuts?

[eldon]

Draw a circle from the centre of the upper donut A to the centre of the lower donut B. Offset the arc at C by the radius of the lower donut. Where these two meet at X is the centre of the lower donut.

[marlon]

Thanks dawg!