These are high school geometry class questions, at least for the graphical construction required.
If you did not take them or do not recall them, I'd suggest looking at the material in Kahn Academy; free and no sign-up required, though if you do sign up it will keep track of your progress.
The first one, may have two circles located on the circumference of the two circles stipulated depending on the location of circles A and B.
The second problem, the circle will lie on the perpendicular bisector of the lines between A and B and C and D, if they intersect, and they could be two different circle radii.
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So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates
When I use 2D AutoCAD or LibreCAD, I systematically maintain at least one sketch layer, which I systematially turned off for printing. Your geometry is easily defined with rectangles in a sketch layer. Snap your circles to the rectangle corners.
