If you are given the triangle, it is a simple matter to construct a circle around it: simply construct the perpendicular bisector of any 2 sides to find the center of the circle.
If the circle is given with no other conditions, simply lay off 3 unequal arcs on the circumference and join the endpoints of those arcs.
If you are given the co-ordinates of the triangle, the analytic solution is a bit messy, but follows the same logic as the geometric construction. You have to get the equations for the perpendicular bisector of any 2 sides and solve them as a simultaneous set; this gives you the co-ordinates of the center. Then use the distance formula from the center to any point to get the radius. Then the circle is (x-h)2 + (y-k)2 = r2 where (h,k) is the center and r is the radius.
