To the many replies (/sarcasm), I figured this out on my own. Turns out the Fillet Tool was useful in itself. The tool inserts a tangent curve fillet dynamically. Since I was using a LARIAC image of the airport, I could simply place the correct radius curve visually. I didn't need to know the curve radius to do what I needed to do as this shape file was to be a simplified visual portrayal of the airport surfaces and not an exacting construction plan.
However, I still have not found a manner in which to place a circle by edge in ArcMap.
