The radius of the circle having centre at (2,1) whose one chord is the diameter of the circle x2 +y2 -2x-6y+6=0

x²+y²-2x-6y+6=0

or, (x²-2x+1)+(y²-6y+9)-4=0

or, (x-1)²+(y-3)²=2²

thus the radius of the smaller given circle is 2 and its centre is (1,3).

distance b/w the two centres = (1+4)^1/2 = 5^1/2

thus the radius of required circle = (5 + 4)^1/2 = 3.