vector - How to place a perfect curve to join two circles together?

I have two circles in this position

I'm looking to acheive this (but more perfect with the flow of the curve meeting the circle perfectly on the right) notice, that it is slightly off)

How would I be able to do this that the three curves when whole are perfect circles?

I am using Corel Draw, but can also do this in Illustrator.

Sizes of the circles and positioning

Answer

Measure the radi/diameters of your circles.

1. Decide on a radius(diameter for the connecting curve, the higher this value the less curved the connection is.


2. Draw a circle with the desired diameter + the diameter (or 2 * radius) of the upper circle, centered on the upper circle center.


3. 
   

   Draw a circle with the desired diameter - the diameter (or 2 * radius) of the lower circle, centered on the lower circle center.

   
   

   

   
   


4. 
   

   The center of the new circle is at the intersection point of these 2 circles with the radius you decided in step 1.