I hope this reply doesn't come too late ...

1. You have determined the intercepts

P(4,0,0), Q(0,2,0) and R(0,0,8)

2. The lines PQ, QR and PR must be tangents to the circle in question. The radius is the perpendicular distance of the center C(1,1,2) to a line.

3. Calculate the 3 perpendicular distances. The shortest of these distances is the greatest radius such that the circle is placed completely in the first octant.