Do you have auto constraints ON or OFF?
I often prefer to set constraints myself.
Draw first circle (you may want to set the diameter and lock the origin of it)
Draw second circle (do same)
Now draw a line between the two circle lines (snapping to the lines)
Click on a circle, then shift click on the line, then set Tangent constraint.
The line will adjust to the tangent position.
Repeat for other circle.
If you find that happening, always remember you can lock a point of the geometry.
Useful on circle centres.
But remember that if you want to move elements of a sketch you will have to unlock those points.
By default you select the item you dont want to move first then the second item you choose is the one that adjusts.
Constraints are really useful, and you can acheive lots with them.
I did also mention in the second post that by default you select the item you dont want to move first.
You can of course change which is the Anchored Sketch entity in constraint settings.
That is another useful video for constraints and the flexibility they bring.
Actually that part was what I wanted to clarify, thinking in order of step 1 and step 2, but logic is the same, because order doesn’t matter if you have locked it already.