Product: MDT 2.x 3.x, 4.x, 5, 6 (7?)

Q: How do I make a Workplane Tangent to a Cylinder? (3503)

A: Lets firstly explain that a workplane honours its placement rules when the model changes, so the plane we will place here will always remain Tangent to the cylinder, even if the cylinder size changes afterwards.

First off we will assume that the cylinder's axis in in the world Z direction as outlined in the figure below.

At the command line enter AMWORKPLN (or use use the button, menu or RClick options to issue the command).
In the Work Plane Feature box select:
  1st Modifier as "Tangent" and
  2nd Modifier as "Planar Parallel"
Check theCreate Sketch Plane box is ticked and click 'OK'.

At the first prompt:

Select cylindrical or conical face: (select the cylinder's face at the cursor location shown below)

At the next prompt:

Select work plane, planar face or [worldXy/worldYz/worldZx/Ucs]:

In my case I enter "Y" to make it parallel to the world YZ plane.

Once placed you can rotate, flip etc. to suit.

Alternatively you could have reversed the order of the selections for the first and second modifiers for the same outcome. That is you could have selected:
  1st Modifier as "Planar Parallel" and
  2nd Modifier as "Tangent"
Check theCreate Sketch Plane box is ticked and click 'OK'.

AJ's Observations
It felt disconcerting picking the cylinder face by picking in the open area indicated in the pic and I probably would always choose to pick on one of the verical isobars that visually define the cylinder walls but this is a personal problem. When I repeated the exersize reversing the choice of modifiers I used shaded mode and felt more comfortable picking the spot indicated because, with the shading, it "felt" like I was picking the cylinder face.
Note that the UCS or three World selection options (in the 1st Modifier) were not used. I read elswehere that you should only use them as a last recourse.
Also note it all worked with DISPSILH=0 (the default) although it is necessary to set DISPSILH to 1 to be able to pick the cylinder wall "edge" for example when it a cylinder is a component of a part you are working on that you want to constrain or dimensioning to.