There are many ways to construct circles and I need a few of them. Here are my questions:

In omnigraffle:

How can I construct a circle given a center and radius?

How can I reference/snapto the center of a circle?

How can I construct a circle given two lines and a radius?

How can I construct a circle given three points on the perimeter?
There are other geometric construction methods that are useful but not needed at the moment but would be worthwhile knowing how to apply.

I am looking for a solution that involves me identifying those reference points/lines in Omnigraffle and the tool figuring out the geometry, not pre-calculating the bounding box. Any assistance would be greatly appreciated.

With the circle selected as your shape, Command + Shift lets you drag out an exact circle. If you have your geometry inspector up, you can use that to set the exact size. You get the Height & Width of the circle as you drag, so it shouldn’t be too tough to know the size. You can also go into your geometry inspector when the item is selected and tweak it to specific values after you have created the basic shape. Specify what you want to scale in the Geometry inspector.

The Alignment options in the Inspector allow you to reference the center point of a circle as it relates to other selected items, or if you choose, to the canvas.

You can also use the Bezier line type with the line tool for plotting points and later editing each point including the handles for defining the curve. In addition, under Edit>Objects you can combine, subtract, intersect, and unite multiple shapes as needed.

Use the Point Editor tool in Pro for tweaking if you need to change points around the perimeter. You can also the specify values in the geometry inspector with individual points if needed to move them to a specific location. If I’ve misunderstood your intent here, I hope by trying these options you can find the parts that you need.