By using a Lathe operation to form the round stuff you will have a set of lines in the axial direction along the surface. In the Lathe group then just add a line with some perpendicular constraints (this will become tangent to the circle) and use that along with one other line and point to define a workplane.

You could probably constrain some lines in 3D with your extruded circles to define the workplane too.

Another option is to use Revolve instead of Lathe. Take it past 360 degrees (450) and you will have 2 sets of axial lines on the surface - you can constrain them perpendicular too. This is an odd technique I use sometimes to get more sketch entities to build things from.

Also, Since the hole is in a plane tangent to the cylinder, using a subsequent rotate group (for multiple radial holes) might fail. In that case, make the extruded hole "double sided" so the surface doesn't end right at the outer surface. This will be more likely to rotate without failure.