What you are looking for is the circumcircle of a triangle. The circumcircle of a triangle is the circle that passes through all three vertices of the triangle and is unique. Help
Although I think you are not looking for the math behind, here, you can find the math to reach to center and radius of a circumcircle from three points (a triangle).
The good news is that ArcObjects has interface to calculate a circumcircle. It is located in TIN related assemblies which is ITinTriangle.QueryCircumCircle
To use this interface you should first create an in-memory TIN:
Here is a C# code. This code is not tested and may have runtime errors
// Instantiate a new empty TIN.
ITinEdit TinEdit = new TinClass();
// Initialize the TIN with an envelope. The envelope's extent should be set large enough to
// encompass all the data that will be added to the TIN. The envelope's spatial reference, if
// if has one, will be used as the TIN's spatial reference. If it is not set, as in this case,
// the TIN's spatial reference will be unknown.
IEnvelope Env = new EnvelopeClass();
Env.PutCoords(0, 0, 10, 10);
// Add points to the TIN. These will become triangle nodes.
IPoint Point = new PointClass();
Point.X = 2;
Point.Y = 2;
Point.Z = 0;
Point.Y = 7;
Point.X = 7;
var tinAdv = TinEdit as ITinAdvanced;
var tri = tinAdv.GetTriangle(0);
IPoint pt = new PointClass();
double r = 0;
Sorry, I don't know VB.NET, use code converters to convert it.